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RESPONSE OF LIQUID XENON TO LOW-ENERGY IONIZING RADIATION ANDITS USE IN THE XENON10 DARK MATTER SEARCH
By
AARON GOSTA MANALAYSAY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2009
1
c© 2009 Aaron Gosta Manalaysay
2
To my Parents
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ACKNOWLEDGMENTS
My time as a graduate student has been a bit atypical, spanning six cities in four
countries on two continents, beginning and ending in The Swamp. It is therefore not
surprising that I have benefited from interactions with a large number of people.
I thank my student colleagues at UF with whom I went through the grad physics
courses and teaching. Guneeta, Shawn, Jesse, Tony, Corey, Dan, Alix, Dana, and Larry.
Getting through those first couple years would have been unbearable without your
friendship and kindness. I thank Zsolt Marcet for running around campus to submit the
first draft of this document by the deadline while I was still in Zurich.
The physics department machine shop, Bill Malphurs and Marc Link in particular,
have been amazing in their skill and professionalism. Without their hard work, much of
the results reported in this dissertation could not have been completed. You are truly
master artists. Darlene Latimer routinely rose above and far beyond her duties in order to
help me. In particular, my transition from continent to continent would have failed if not
for her assistance and dedication. You have been invaluable to me in my time as a grad
student, and indeed to the Department you are irreplaceable. I thank David Hansen for
helping me to finally and forever shed my dependence on Windows, and assisting me with
the many computer problems I had along the way.
My fellow XENON10 grad students and post-docs with whom I worked in Gran Sasso
made my time there very enjoyable and productive. I thank Kaixuan for the Redstar,
John, Angel and Eric for the billiardino matches. Luiz, Eric and Peter created a wonderful
atmosphere in the apartment and in Hall di Montaggio. Go matlab! Peter, having you
next to me going through the same “patience-improvement” program was a life saver.
Eric, I think I acquired much of my knowledge of LXe physics theory from conversations
with you; it’s a shame you’ve left the field, but good luck with your bubbles. Joerg
Orboeck was a pleasure to work with, both in Florida and Italy. Alfredo Ferella, the
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Prince of Paganica, has greatly enhanced my life as a Ph.D. student, both in Italy and in
New York. Next time we drive a stolen van through Brooklyn, let’s bring a map.
I thank Elena Aprile for generously inviting me to work in her lab at Columbia
University, the results of that summer constituting one chapter of this dissertation. I
additionally benefited tremendously from working with Masaki Yamashita both in New
York and in Gran Sasso. Your ability to complete the work of five people always amazes
me, and inspires me to hope that I can one day be half the physicist you are.
The Physik Institut Sekretariat, in particular Ruth Halter and Monika Rollin,
make everyone’s lives nicer, mine especially. Coming into a new place as a foreigner, not
knowing the language, nor the system, is an intimidating prospect; I thank Ruth and
Monika for making my days in Zurich easy.
John Yelton and Alan Dorsey made great efforts in order that I could move to Europe
while simultaneously remaining a UF student and also continue to receive a salary. They
additionally pulled many strings so that the detector I starting building at NPB could join
me on the trip.
My student and post-doc colleagues at Universitat Zurich, Alex, Ali, Eirini, Teresa,
Annika, Tobias, Sebastian, Marijke, Michael, Francis, Roberto, and Marc have made my
work there fun and enjoyable. Eirini, you were wonderful as my partner in homelessness
during the first few months before any of us had apartments; you were one of the nicest
roommates I have ever encountered. Kαλη τ υχη στην Kρητη! Teresa, I have enjoyed the
many discussions we have had about scintillators, data analysis, office politics, and even
linguistics; muchas gracias.
My many friends in Zurich with whom I did not work, nonetheless made my working
time enjoyable. Spending time with the [mostly Auslander] astro group upstairs, especially
for Tuesday pizza, is always tons of fun. I thank Tina for introducing me to Flims,
Muse, and Mehr Spur, and Dominik for showing me that I really need to improve my
snowboarding skills if I am living in Switzerland. I also enthusiastically thank Aaron and
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Karen Boley for welcoming me into their home during my return to Gainesville for writing
and defending. You guys rock!
To Laura Baudis, my Professor, teacher, and mentor, I express my gratitude, for
the opportunities, experience, and knowledge with which you have provided me, and the
patience you have that has accompanied your instruction. You have afforded me countless
experiences that have changed me. Danke fur alles.
Finally, I thank my parents, to whom this work is dedicated. Your guidance has
set me on the right path, your encouragement has given me motivation to succeed, your
support has helped me in times of uncertainty and doubt, and your love has crafted me
into the person I am today. I love you both.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
CHAPTER
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2 Evidence for Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.2.1 Galactic Scale - Rotation Curves . . . . . . . . . . . . . . . . . . . . 201.2.2 Cluster Scale - Cluster Redshift Surveys . . . . . . . . . . . . . . . . 211.2.3 Cluster Scale - Gravitational Lensing and Intracluster Plasma . . . 231.2.4 Cluster Scale - Clusters Mergers . . . . . . . . . . . . . . . . . . . . 251.2.5 Cosmological Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.3 Dark Matter Candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.3.2 Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291.3.3 Thermal Freeze-Out and the Weakly Interacting Massive Particle . . 31
2 DIRECT DETECTION AND LIQUID XENON . . . . . . . . . . . . . . . . . . 35
2.1 The Local Dark Matter Environment . . . . . . . . . . . . . . . . . . . . . 352.2 WIMP Interaction Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Spin-Independent Interactions . . . . . . . . . . . . . . . . . . . . . 372.2.2 Spin-Dependent Interactions . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Direct Detection Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.1 Examples of Direct Detection Experiments . . . . . . . . . . . . . . 402.3.2 Why Liquid Xenon? . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4 Liquid Xenon Interaction Physics . . . . . . . . . . . . . . . . . . . . . . . 442.4.1 Microscopic Processes in a Particle Track . . . . . . . . . . . . . . . 442.4.2 Lindhard Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . 462.4.3 Putting it All Together: Leff . . . . . . . . . . . . . . . . . . . . . . 47
3 THE XENON10 EXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1 The XENON10 Detector and Underground Facility . . . . . . . . . . . . . 493.1.1 Detector Description . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1.2 Laboratori Nazionali del Gran Sasso . . . . . . . . . . . . . . . . . . 513.1.3 Nuclear Recoil Discrimination . . . . . . . . . . . . . . . . . . . . . 52
3.2 Electronic Recoil Band Shape . . . . . . . . . . . . . . . . . . . . . . . . . 58
7
3.2.1 Activated Xenon and the Combined Energy Scale . . . . . . . . . . 593.2.2 Monte Carlo Construction . . . . . . . . . . . . . . . . . . . . . . . 613.2.3 Monte Carlo Results . . . . . . . . . . . . . . . . . . . . . . . . . . 633.2.4 Energy Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3 WIMP Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.3.1 Spin-Independent Interaction . . . . . . . . . . . . . . . . . . . . . . 703.3.2 Spin-Dependent Interactions . . . . . . . . . . . . . . . . . . . . . . 733.3.3 Prospects for the Heavy Majorana Neutrino . . . . . . . . . . . . . 77
4 MEASUREMENT OF LEFF WITH THE XECUBE DETECTOR . . . . . . . . 81
4.1 Leff and the Need for its Further Study . . . . . . . . . . . . . . . . . . . . 814.2 Methods for Measuring Leff . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.1 Measurement Technique and Facility . . . . . . . . . . . . . . . . . 824.2.2 The Xecube Detector . . . . . . . . . . . . . . . . . . . . . . . . . . 844.2.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.3.1 Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.3.2 Event Selection, Backgrounds, and Results . . . . . . . . . . . . . . 89
4.4 Indirect Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5 THE XURICH DETECTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.1 TPC Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.2 Auxiliary Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2.1 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.2.2 Gas System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.3 Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.4 Data Acquisition and Signal Processing . . . . . . . . . . . . . . . . . . . . 108
5.4.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.4.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.2.1 Preliminary data manipulation . . . . . . . . . . . . . . . 1115.4.2.2 S2 finding . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.4.2.3 S1 finding . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.5 Liquid Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135.6 LXe Purity and Electron Lifetime . . . . . . . . . . . . . . . . . . . . . . . 116
6 LIQUID XENON CALIBRATION WITH 83RB . . . . . . . . . . . . . . . . . . 120
6.1 The Need for a New Calibration Source . . . . . . . . . . . . . . . . . . . . 1206.2 The 83mKr Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4.1 Light Yield and Field Quenching . . . . . . . . . . . . . . . . . . . . 1316.4.2 Radioactive Background Contamination . . . . . . . . . . . . . . . . 132
8
6.4.3 Other Contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5 Exciton to Ion Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7 PMT STATISTICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.1 Analytic Approach to the Single Photoelectron Spectrum . . . . . . . . . . 1407.2 PMT Monte Carlo and Function Test . . . . . . . . . . . . . . . . . . . . . 1437.3 The Indirect Gain Estimation Method . . . . . . . . . . . . . . . . . . . . 147
8 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
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LIST OF TABLES
Table page
3-1 Nuclear recoil discrimination parameters and background estimates. . . . . . . . 57
3-2 The spin expectation values for proton and neutron groups based on three nuclearshell models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3-3 The polynomial coefficients of a fit to the quasiparticle Tamm-Dancoff spin structurefunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4-1 The Leff results from the neutron beam measurements. . . . . . . . . . . . . . . 94
6-1 Measured light yield and field dependence parameters. . . . . . . . . . . . . . . 126
7-1 Monte Carlo dynode configurations and fit function performance. . . . . . . . . 146
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LIST OF FIGURES
Figure page
1-1 The rotation curve for galaxy NGC 6503 . . . . . . . . . . . . . . . . . . . . . . 21
1-2 The measured mass-to-light ratios, in solar units (M¯/L¯), for a collection ofgalaxy clusters, as a function of their velocity dispersion. . . . . . . . . . . . . . 22
1-3 An example of strong gravitational lensing. . . . . . . . . . . . . . . . . . . . . . 23
1-4 A compilation of the gas fraction of six rich galaxy clusters, as a function ofredshift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1-5 Examples of colliding galaxy clusters. . . . . . . . . . . . . . . . . . . . . . . . . 26
1-6 The predicted relative abundances of light elements from Big Bang nucleosynthesis. 27
1-7 The axion-photon coupling versus axion mass parameter space. . . . . . . . . . 30
1-8 A survey of the interaction cross section versus particle mass for various particledark matter candidates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2-1 The differential recoil spectra of WIMPs in various detector materials. . . . . . . 39
2-2 Ionization yield versus energy in the CDMS-II experiment. . . . . . . . . . . . . 41
2-3 Distribution of the discrimination parameter, MT in the KIMS experiment. . . 42
2-4 Examples of three classes of bubble-creating interactions in the COUPP bubblechamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2-5 Potential energy curves of ground-state argon in proximity to excited or ionizedargon atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3-1 Schematic of the XENON10 detector. . . . . . . . . . . . . . . . . . . . . . . . . 50
3-2 The drift velocity of electrons in xenon as a function of applied electric field. . . 51
3-3 Layout of the Laboratori Nazionali del Gran Sasso . . . . . . . . . . . . . . . . 52
3-4 XENON10 detector and shielding. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3-5 Electronic and nuclear recoil bands in the XENON10 detector. . . . . . . . . . . 54
3-6 The flattened electronic and nuclear recoil bands in XENON10. . . . . . . . . . 55
3-7 Distributions of ∆log10(S2/S1) for nuclear and electronic recoils. . . . . . . . . . 56
3-8 The electronic recoil rejection in XENON10. . . . . . . . . . . . . . . . . . . . . 57
3-9 Decomposition of the electronic recoil band variance. . . . . . . . . . . . . . . . 58
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3-10 Activated xenon and the combined energy scale. . . . . . . . . . . . . . . . . . . 60
3-11 Spectrum of recombination fluctuations from 131mXe. . . . . . . . . . . . . . . . 61
3-12 The photon fraction from low-energy 137Cs Compton scatters and the comparisonof data to MC in log10(S2/S1) versus S1. . . . . . . . . . . . . . . . . . . . . . . 62
3-13 Low-statistic comparison of data to MC of ∆ log10(S2/S1). . . . . . . . . . . . . 63
3-14 High-statistic comparison of data to MC of ∆ log10(S2/S1). . . . . . . . . . . . . 64
3-15 Gaussian rejection versus MC rejection. . . . . . . . . . . . . . . . . . . . . . . . 65
3-16 MC-based corrections to 1−Rer and Nleak. . . . . . . . . . . . . . . . . . . . . 65
3-17 Mapping of a symmetric interval in photon-fraction into an asymmetric intervalin log10(S2/S1) space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3-18 Lines of constant S1 and their span in CES. . . . . . . . . . . . . . . . . . . . . 67
3-19 High-statistic comparison of data to MC of ∆ log10(S2/S1) for various energyranges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3-20 Corrections to Nleak given by the MC applied to all energies. . . . . . . . . . . . 69
3-21 Evolution of the live time of the XENON10 blind data. . . . . . . . . . . . . . . 70
3-22 XENON10 WIMP search data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3-23 XENON10 exclusion curve on the spin-independent WIMP-nucleon cross section. 72
3-24 The quasiparticle Tamm-Dancoff spin structure functions and polynomial fits. . 75
3-25 Pure proton and pure neutron XENON10 spin-dependent exclusion limits. . . . 76
3-26 The WIMP-neutron exclusion limit calculated for four different combinations of129Xe and 131Xe shell models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3-27 XENON10 C0 as a function of mass for the heavy Majorana neutrino. . . . . . . 79
4-1 A survey of Leff measurements in the literature prior to 2009, along with theenergy ranges relevant for the XENON10 and Zeplin-II experiments. . . . . . . . 81
4-2 The XENON10 spin-independent WIMP-nucleon cross section with its uncertaintydue to Leff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4-3 Schematic diagram of the neutron beam experiment. . . . . . . . . . . . . . . . 83
4-4 Schematic diagram of the Xecube detector. . . . . . . . . . . . . . . . . . . . . . 85
4-5 Schematic diagram of the data acquisition system used with the Xecube detector. 86
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4-6 The efficiency of the Xecube trigger. . . . . . . . . . . . . . . . . . . . . . . . . 87
4-7 Spectrum from 57Co in Xecube. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4-8 Distribution of events in pulse shape parameter versus time of flight. . . . . . . 90
4-9 Selected results of Monte Carlo simulations of the neutron beam measurements. 91
4-10 Spectra of events from the neutron beam measurements. . . . . . . . . . . . . . 93
4-11 Measured Leff values as a function of Xe nuclear recoil energy. . . . . . . . . . . 95
4-12 Real and simulated spectra of elastic neutron scatters from AmBe in the Xecubedetector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4-13 The XENON10 spin-independent WIMP-nucleon cross section exclusion limitusing Leff from this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5-1 Diagram of the Xurich dual-phase time projection chamber. . . . . . . . . . . . 102
5-2 Spectrum from 57Co at zero field in the Xurich detector. . . . . . . . . . . . . . 103
5-3 The cryostat used for the Xurich detector. . . . . . . . . . . . . . . . . . . . . . 104
5-4 Cryostat performance over roughly one month. . . . . . . . . . . . . . . . . . . . 105
5-5 The gas system in charge of Xe filling, purification, recovery, and storage. . . . . 106
5-6 One of the photomultiplier tubes used in the Xurich detector. . . . . . . . . . . 107
5-7 Single photoelectron spectra from Xurich’s photomultiplier tubes at varying appliedcathode voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5-8 Schematic of the data acquisition system. . . . . . . . . . . . . . . . . . . . . . . 109
5-9 Measured and simulated trigger efficiency of the Xurich detector. . . . . . . . . 110
5-10 An example raw PMT output trace from an event in dual-phase mode. . . . . . 112
5-11 The calculated S2 gain as a function of gas gap. . . . . . . . . . . . . . . . . . . 114
5-12 The spectra of S2 at various azimuthal positions before leveling the detector. . . 115
5-13 The spectra of S2 at various azimuthal positions after leveling the detector. . . . 115
5-14 The rate constant for attachment of electrons on O2, N2O, and SF6 in LXe as afunction of applied field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5-15 S2 versus drift time before and after purification. . . . . . . . . . . . . . . . . . 118
5-16 Evolution of the electron lifetime over the course of one week of purification. . . 118
6-1 The decay scheme and branching ratios of 83mKr. . . . . . . . . . . . . . . . . . 122
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6-2 Area of the first S1 pulse versus the area of the second with and without the83mKr source. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6-3 Distribution of delay times between first and second S1 pulses. . . . . . . . . . . 125
6-4 Field quenching of three spectral lines in liquid xenon. . . . . . . . . . . . . . . 127
6-5 Spectra for the line at 41.5 keV in S1, S2, and combined energy. . . . . . . . . . 129
6-6 Rate of 83mKr decays as a function of z-position. . . . . . . . . . . . . . . . . . . 130
6-7 Constraints on Nex/Nion and χ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6-8 The inverse charge collection versus the inverse applied electric field of the 41.5 keVline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6-9 S1 versus S2 shown for the 41.5 keV line taken at various applied fields, showingthe anticorrelation of the two signals. . . . . . . . . . . . . . . . . . . . . . . . . 138
7-1 Schematic diagram of a photomultiplier tube. . . . . . . . . . . . . . . . . . . . 139
7-2 Analytic probability distribution of a photomultiplier tube output. . . . . . . . . 142
7-3 An example of real PMT single photoelectron spectra. . . . . . . . . . . . . . . 143
7-4 Sample of simulated Monte Carlo SPE spectra. . . . . . . . . . . . . . . . . . . 145
7-5 Distribution of gain estimators. . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7-6 Spectra of PMT output from varying the LED intensity. . . . . . . . . . . . . . 148
7-7 Variance versus mean from varied LED illuminations. . . . . . . . . . . . . . . . 149
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Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy
RESPONSE OF LIQUID XENON TO LOW-ENERGY IONIZING RADIATION ANDITS USE IN THE XENON10 DARK MATTER SEARCH
By
Aaron Gosta Manalaysay
December 2009
Chair: John YeltonCochair: Laura BaudisMajor: Phyiscs
This dissertation focuses on developments aimed at improving the effectiveness and
understanding of liquid xenon particle detectors in their use in the field of dark matter
direct detection. Chapter 3 covers the XENON10 experiment, which searches for evidence
of direct interactions between Weakly Interacting Massive Particles (WIMPs) and Xe
nuclei. The 3-D position sensitive liquid xenon time projection chamber acquired 58.6
live days of WIMP search data from October, 2006 through February, 2007. The results
of these data set new limits on both spin-independent and spin-dependent interactions.
The spin-independent WIMP-nucleon cross section is constrained to be less than 4.5 ×10−44 cm2 for WIMPs of mass 30GeV/c2 and less than 8.8 × 10−44 cm2 for WIMPs of
mass 100GeV/c2 at the 90% confidence level. The spin-dependent WIMP-neutron and
WIMP-proton cross sections are constrained to be less than 10−39 cm2 and 10−36 cm2,
respectively. Finally, the mass of the heavy Majorana neutrino, in the context of a dark
matter candidate, is excluded for masses in the range 10GeV/c2 to 2.2 TeV/c2.
Chapter 4 discusses the study of the relative scintillation efficiency of nuclear
recoils in liquid xenon. The two existing measurements of the relative scintillation
efficiency of nuclear recoils below 20 keV lead to inconsistent extrapolations at lower
energies. This results in a different energy scale and thus sensitivity reach of liquid
xenon dark matter detectors. A new measurement of the relative scintillation efficiency
15
below 10 keV, performed with a liquid xenon scintillation detector and optimized for
maximum light collection is discussed. Greater than 95% of the interior surface of this
detector was instrumented with photomultiplier tubes, giving a scintillation yield of 19.6
photoelectrons/keV electron equivalent for 122 keV gamma rays. The relative scintillation
efficiency for nuclear recoils of 5 keV is found to be 0.14, staying constant around this
value up to 10 keV. For higher energy recoils we measure a value of 0.21, consistent with
previously reported data. In light of this new measurement, the XENON10 experiment’s
upper limits on spin-independent WIMP-nucleon cross section, which were calculated
assuming a constant 0.19 relative scintillation efficiency, change from 8.8 × 10−44 cm2 to
9.9×10−44 cm2 for WIMPs of mass 100GeV/c2, and from 4.5×10−44 cm2 to 5.6×10−44 cm2
for WIMPs of mass 30GeV/c2.
In Chapter 6, I highlight the fact that a difficult task with many particle detectors
focusing on interactions below ∼100 keV is to perform a calibration in the appropriate
energy range that adequately probes all regions of the detector. Because detector response
can vary greatly in various locations within the device, a spatially uniform calibration is
important. A new method for calibration of liquid xenon (LXe) detectors is presented,
using the short-lived 83mKr. This source has transitions at 9.4 and 32.1 keV, and as a
noble gas like Xe, it disperses uniformly in all regions of the detector. Even for low source
activities, the existence of the two transitions provides a method of identifying the decays
that is free of background. At decreasing energies, the LXe light yield increases, while the
amount of electric field quenching is diminished. Additionally, if any long-lived radioactive
backgrounds are introduced by this method, it is shown that they will present less than
67×10−6 events kg−1 day−1 keV−1 of background in the next generation of LXe dark matter
direct detection searches.
16
CHAPTER 1INTRODUCTION
Without Isaac Newton, we’d be floating on the ceiling.
-Dr. Gregory House
1.1 Introduction
The study of the cosmos has captivated the interests of our species for longer than
the written tradition has recorded our lives. The desire to observe, predict, and most
importantly, understand the behavior of objects in the night sky has fueled many of
the innovations in mathematics, science, and technology that have born the fruit of our
modern way of life.
The improvements in our understanding of cosmology during and following the
Renaissance culminated in Newton’s laws of motion, and equally important, in his law of
universal gravitation, which gives the force, F , exerted between two objects of mass m1
and m2 separated by a distance r as,
F =GNm1m2
r2, (1–1)
with constant of proportionality, GN , known as Newton’s gravitational constant. With this
one simple mathematical relation, Newton was able to quantitatively explain the observed
motions of the planets, moons, and comets. However, the theory did more than just this;
it was extremely important in advancing the Copernican principle, a central tenet of
modern cosmology, that Earth occupies no central or special place in the Universe. For
the first time, it provided an unequivocal statement that the physical laws governing
the behavior of the heavens are the same as those governing events on Earth. This was
in stark contrast to the most accurate cosmological model prior to Newton: Ptolemy’s
geocentric theory of planetary epicycles [1].
Newton’s law of gravitation finally closed forever any possibility of an adherence to
a geocentric cosmology, and in doing so, expanded the scale of the observable universe
17
by orders of magnitude. For if now the Earth orbits the sun, the “fixed” stars must be
very far away if they are to exhibit no apparent proper motion throughout the year.
But while Newton’s theory enjoyed much success in quantitative accuracy, it suffered in
that it provided no explanation or mechanism for its implicit instantaneous “action at
a distance”. The solution to this problem took centuries, until Einstein revolutionized
our understanding of gravity as a geometrical effect, resulting from the curvature of
space-time. This curvature is quantified by the metric tensor, gµν , that defines a rule
for calculating the distance between points on our space-time manifold by the relation,
ds2 = gµνdxµdxν . It is the dynamic variable in Einstein’s field equations,
Rµν − 1
2gµνR = −8πGN
c4Tµν + Λgµν , (1–2)
where Rµν and R are the Ricci tensor and scalar (formed from second derivatives of gµν),
respectively, c is the speed of light in vacuum, Tµν is the stress-energy tensor, and Λ is the
cosmological constant (written on the right-hand side in this way, it acts as a source of
curvature, as opposed to an intrinsic curvature as originally imagined by Einstein). This
is, at face value, much less simple than Newton’s universal gravitation (equation 1–1).
The space-time indices, µ and ν, run from 0 to 3, and hence the tensors in equation 1–2
contain sixteen elements. Although these elements are not all independent due to the
symmetry of gµν , we are still left with ten independent, nonlinear, second-order, coupled
differential equations. Exact solutions to equation 1–2 are rare, and can only be made in
systems that exhibit high degrees of geometric and temporal symmetry.
Cosmologists exploit the Copernican principle and the fact that the Universe appears
to be homogeneous and isotropic on large scales (&100Mpc). With these symmetries, the
solution to equation 1–2 is given by the Friedmann-Lemaıtre-Robertson-Walker (FLRW)
metric, whence the invariant line element in spherical coordinates is,
ds2 = −c2dt2 + a2(t)
(dr2
1− kr2+ r2dΩ2
), (1–3)
18
where a(t) is the scale factor, and k, describing the spatial curvature, can take the values
of -1, 0, +1 for open, flat, and closed universes, respectively. a(t) is related to the Hubble
parameter quantifying the expansion rate of the universe, H, by the relation,
H(t) =a
a, (1–4)
with the dot denoting the derivative with respect to coordinate time.
Inserting the FLRW metric back into equation 1–2, and taking the 00 component
gives the Friedmann equation,
H2(t) +k
a2=
8πGN
3ρtot, (1–5)
where ρtot is the total energy density of the Universe. Using this equation, we can then
solve for the critical density, ρc, that is required to force the universe to be exactly flat (i.e.
k = 0):
ρc =3H2
8πGN
. (1–6)
With this definition, we can then express the content of the universe (i.e. the sources that
go into Tµν) in terms of their densities relative to ρc, by,
Ωi ≡ ρi
ρc
, (1–7)
where the subscript i labels the various components. The total energy density of the
universe, Ω, is given as Ω ≡ ∑Ωi. A remarkable discovery of the past century has been
that Ωbaryons ¿ Ω. That is, the visible matter that we see in telescopes accounts for only
a small fraction of the total energy content of the Universe. The majority (∼70%) of this
invisible energy appears to be in the form of vacuum energy, while the remaining ∼30% is
mostly a form of invisible matter, called dark matter. In the next section I discuss some
of the many pieces of evidence for dark matter, and then finally highlight some candidates
that arise in particle physics.
19
1.2 Evidence for Dark Matter
It has become increasingly apparent that most of the matter in the universe is unseen,
“dark”, in observations of electromagnetic radiation. What started as astronomical
discrepancies observed by Zwicky of the Coma cluster in 1933 [2], and later by Volders
of M33 in 1959 [3] and by Rubin of M31 in 1970 [4], have evolved into scores of evidence
that all point to the fact that roughly 98% of the matter in the universe is non-stellar,
and roughly 85% is nonbaryonic [5]. I discuss some of this evidence, from galactic scales to
cosmological scales.
1.2.1 Galactic Scale - Rotation Curves
On the scale of individual galaxies, the motion of the stars and gas can be used to
probe the underlying mass profile influencing their motion. This is typically done by
observing spiral galaxies that are nearly edge-on from our perspective, and measuring
the redshift as a function of distance from the center. The light coming from the stars
themselves can be used for this purpose, but a clearer measurement can be done by
observing the 21 cm emission of neutral hydrogen [6]. The cloud of neutral hydrogen
typically extends far beyond the visible disk of stars, and hence can probe more of the
galaxy than the stars themselves. Measurements of this type then allow one to construct
a rotation curve of the galaxy, which is simply a plot of the rotational velocity of the
galactic material as a function of the distance, r, from the galactic center. Newtonian
dynamics predicts the rotation curve based on the total mass, M(r) located inside r,
v(r) =
√GNM(r)
r(1–8)
What is found in virtually all galaxies is that the rotation curve is characteristically
flat at large radii (i.e. outside of the central ‘bulge’). The stellar density of spiral galaxies
typically falls of exponentially in these regions, and alone cannot account for the observed
rotation curves. Including the hydrogen gas (which emits the 21 cm radio waves used
to measure the rotation curves) does not solve the problem either. Figure 1-1 shows
20
Figure 1-1. The rotation curve for galaxy NGC 6503, showing the expected contributionfrom the disk and gas. The measured values (data points) require anadditional contribution from a non-luminescent halo. Figure taken from [6].
the rotation curve of galaxy NGC 6503. The matter content of the disk and gas can be
measured, and their expected contributions to the rotational velocity predicted using
equation 1–8. The measured values (data points) require the addition of an additional halo
of material not visible with telescopes.
1.2.2 Cluster Scale - Cluster Redshift Surveys
The first evidence for extra matter in the cosmos came from Fritz Zwicky by making
observations of the motion of galaxies within the Coma Cluster [7]. The line-of-sight
velocity of these galaxies is obtained by measuring their redshifts. Using these measured
velocities, Zwicky then calculated the total gravitational potential using the virial
theorem,
2〈T 〉 = −〈Vtot〉, (1–9)
where T is total kinetic energy, Vtot is the total gravitational potential energy, and the
angle brackets denote the average over time.
21
This measurement by itself must be compared to the total mass expected from the
stars in the galaxies alone. For this, the mass-to-light ratio, Y is calculated. This value
is normalized such that the Sun’s mass-to-light ratio, Y¯, is unity. Strict deviation of the
cluster from Y=1 does not indicate discrepancy, because of course one is measuring vast
conglomerations of many stars, and our Sun’s own mass and luminosity are not necessarily
representative of exact averages of large stellar populations. However, recent studies of the
Coma Cluster indicate that Y=182 [8]. This result, that Y À 1, implies the presence of
large quantities of additional, invisible mass.
Figure 1-2. The measured mass-to-light ratios, in solar units (M¯/L¯), for a collection ofgalaxy clusters, as a function of their velocity dispersion. The extremedeviation of these values from unity is a clear indication that more matterexists in the clusters than simply the stars and gas observable by telescopes.Plot taken from [9].
The anomalous value of Y indicated above is not limited to the Coma cluster. In fact,
such a large discrepancy is seen in every galaxy cluster in which it is measured. A survey
over many galaxy cluster has found an average cluster value of Y= 240± 50 [9, 10]. These
results imply that Ωcluster = 0.19± 0.07 [10].
22
1.2.3 Cluster Scale - Gravitational Lensing and Intracluster Plasma
Figure 1-3 (left) shows a dramatic example of gravitational lensing. In situations
like these, the light emitted from a distant galaxy (the “lensed object”) is bent by the
gravitational well of a galaxy cluster (the “lens object”) lying directly between the Earth
and the distant galaxy. The space in the vicinity of the lensing cluster is curved in such a
way that as the light from the distant galaxy follows geodesics, deviates from a straight
line and then reaches the Earth from multiple points in the sky, producing a series of
warped images.
Figure 1-3. (Left) A stunning example of gravitational lensing visible in the Abell 370galaxy cluster, located in the northern constellation Cetus. The bright yellowgalaxies visible throughout the field are members of the lensing cluster,producing the multiple, distorted images of the red-blue background galaxy.(Right) A reconstruction of the mass profile in the galaxy CL 0024+1654based on strong gravitational lensing. This cluster lies roughly 5 billionlight-years away in the constellation Pisces. The spikes in the mass profilemark the individual galaxies, however, it is clear that an additional collectionof mass lies between the galaxies. Figure taken from [11].
Observations of gravitational lensing are a confirmation of Einstein’s theory of general
relativity. But more than that, they can be used to probe the distribution of mass within
the lensing cluster [12]. The cluster CL 0024+1654 acts as a lens of a single background
galaxy, located roughly 10 billion light-years away. Using the multiple images of this
background galaxy, it is possible to calculate the mass-to-light ratio, Y of the lensing
23
cluster to be Y= 276± 40 [13], in accord with the velocity dispersion measurements of the
last section.
While the measurement of Y is indicative that additional matter exists in the clusters
than just the stars, it does not rule out the possibility that the extra mass is in the
form of some other, non-optically-luminous, but baryonic, component. Indeed, galaxy
clusters contain large quantities of hot, x-ray emitting plasma. While the density of
this intracluster plasma is very low, on the order of 10−26 g cm−3, it is not bound to the
individual galaxies and instead smoothly pervades the whole cluster. Therefore, the total
plasma mass can be quite large, and in fact exceeds the mass of luminous material by a
factor of ∼6 [14].
Figure 1-4. A compilation of the gas fraction of six rich galaxy clusters, as a function ofredshift. The mass fraction is defined as the fraction that intracluster plasmacontributes to the total mass of the cluster. The intracluster plasmaconstitutes the majority of baryonic matter in a galaxy cluster, and hence anadditional, nonbaryonic component is needed to account for the fact thatfgas < 1. Figure taken from [15].
The luminosity of the plasma in x-rays is proportional to the square of the density,
and therefore the plasma mass of a cluster can be determined from observations with
x-ray telescopes. When these measurements are combined with measurements of the total
cluster mass from gravitational lensing, a determination can be made of the gas fraction,
24
fgas, defined as the fraction that the plasma contributes to the total cluster mass. Allen
and others have compiled such measurements for a sample of six rich galaxy clusters,
seen in Figure 1-4 as a function of redshift. The weighted average of these results give
fgas = 0.113± 0.005 [15].
1.2.4 Cluster Scale - Clusters Mergers
Perhaps the most clear-cut and unmistakable signal of dark matter results from
the violent collisions between galaxy clusters. As in Figure 1-3 (right), the dominant
component of a galaxy cluster’s mass is the dark matter. Additionally, there exist vast
clouds of hot, x-ray emitting intracluster plasma. While neither of these two components
are visible in optical wavelengths, they make up the bulk of the cluster mass. The
main difference between the dark matter and the intracluster gas is in their interaction
strengths: gas is collisional, dark matter is not.
Therefore, when two clusters of galaxies collide, the conglomerations of dark matter
will pass right through one another, as they experience mainly gravitational interactions.
The intracluster plasma clouds, however, will interact electromagnetically, and hence will
exhibit very different dynamics during the collision than the dark matter.
Fortunately, due to their different qualities, the different components can be studied
separately. The density and distribution of the plasma can be studied by observing
the x-ray emission [15]. In contrast, the dominant mass of the clusters can be studied
by gravitational lensing, as discussed in section 1.2.3. The results from four examples
of cluster collisions are shown in Figure 1-5. These examples are from (clockwise from
top-right) the Bullet cluster [16], MACS J0025.4-1222 [17], MACS J0717.5+3745 [18],
and Abell 520 [19]. In each example, the extent of cluster plasma (determined from
x-ray emission) is indicated in pink, while the distribution of mass (determined from
gravitational lensing) is indicated in blue.
Most visible in the Bullet cluster and in MACS J0025.4-1222 is that the clouds of hot
gas have been stripped away from their parent clusters. In all other dark matter evidence,
25
Figure 1-5. Examples of colliding galaxy clusters. Clockwise from top-left are shown theBullet cluster [16], MACS J0025.4-1222 [17], MACS J0717.5+3745 [18], andAbell 520 [19]. In each case the intracluster plasma is shown in pink (whichconstitutes the majority of the baryonic mass), while the dominant clustermass is shown in blue. The displacement of one from the other can only beconsistently explained by dark matter.
one is considering discrepancies in the strength of the gravitational force. However,
here the evidence is much more clear: the dominant mass is laterally displaced from the
baryonic matter. Furthermore, the result is consistent with the expectations of collisionless
dark matter.
1.2.5 Cosmological Scales
While the evidence of dark matter on galaxy cluster scales can be generalized to be
representative of the Universe as a whole, more direct evidence of dark matter on truly
26
cosmological scales exists. The first, Big Bang nucleosynthesis (BBN) provides evidence
that Ωb is significantly less than unity.
Figure 1-6. The predicted relative abundances of the light elements, depending on a singleparameter, the baryon-to-photon ratio, η. Measurements of the actualabundances are indicated by the boxes: yellow boxes represent ±2σ statisticaluncertainty on the measurements, larger, dashed boxes represent the ±2σstatistical and systematic uncertainty of the same measurements. The 95%confidence bounds of Ωbh
2 from BBN are marked by the vertical tan lines, andthe measurement of the same parameter from the Cosmic MicrowaveBackground is shown by the text ‘CMB’ . Figure from [20].
The processes by which the light elements are produced in the Big Bang involves
fairly well-studied particle and nuclear physics. The theory very uniquely predicts the
relative abundances of the light elements (3,4He, 2H, and 7Li) and is characterized by a
single parameter, η, the baryon-to-photon number ratio (see Figure 1-6). The predictions
of the model are remarkably consistent with the measurements of the relative abundances,
and give a value of η = (5.6+0.8−0.7) × 10−10 [21]. Combining this with the known density
of photons in the Universe from the cosmic microwave background (CMB) gives the
27
cosmological density of baryons as
Ωbh2 = 0.020+0.003
−0.002, (1–10)
where the subscript b denotes baryons and h is the Hubble parameter (h = H0/100 km s−1 Mpc−1,
H0 = 71.9+2.6−2.7 km s−1 Mpc−1 is the present value of the Hubble expansion rate [22]).
The CMB, the smooth T = 2.726K black body radiation leftover from the Big Bang
has temperature fluctuations at the 10 µK level. These anisotropies are a direct result of
temperature fluctuations at the time when electrons and nuclei first combined to form
neutral atoms. The nature of these fluctuations in turn is very sensitive to the contents
of the universe. The 5-year data of the Wilkinson Microwave Anisotropy Probe (WMAP)
have recently been released, placing tight constraints on a zoo of cosmological parameters.
Of relevance to the present discussion are the density of baryons and total matter, given
as [22],
Ωbh2 = 0.02273± 0.00062, Ωmh2 = 0.1326± 0.0063, (1–11)
showing clear agreement with the results of BBN on Ωb. The value Ωm is the density of all
matter.
1.3 Dark Matter Candidates
1.3.1 Neutrinos
With the knowledge that the dark matter is nonbaryonic, electrically neutral, and
stable, it is natural to first look at the Standard Model (SM) for a potential culprit. The
only SM particles that meet these criteria are the neutrinos. Neutrinos were active in the
early universe and played a role in the formation of light nuclei. Their relic abundance is
given by [7, 23],
Ωνh2 =
∑i
gimi
93 eV, (1–12)
where the index i runs over the number of neutrino generations, gi = 1 for Majorana
neutrinos and 2 for Dirac neutrinos, and mi is the mass of the i-th neutrino. The
independent results of atmospheric and solar neutrino oscillations imply that the heaviest
28
neutrino has a mass mν & 0.05 eV [24, 25]. This implies that
Ωνh2 & 0.0006. (1–13)
The abundance of relic neutrinos can be probed from cosmological measurements.
Prior to their thermal decoupling, large amounts of primordial neutrinos would act to
decrease damping of oscillations in the early photon-baryon plasma, which would increase
the strength of the peaks in the CMB anisotropies. Additionally, the expansion rate of the
universe would be altered, thereby shifting the position of the acoustic peaks. Primordial
neutrinos, decoupling hot, would smooth out structure on small scales (. 40Mpc). This
would imply that large scale structure formed “top-down”, meaning large scales formed
first, with small scale structure forming later. This scenario is unlikely, as the Milky Way
appears to be much older than the local group. These cosmological constraints imply that∑
mν < 0.61 eV (95% C.L.). Using this result with equation 1–12 implies that these
results give an upper limit on the total contribution of neutrinos to be [22],
Ωνh2 < 0.0065 (95%C.L.). (1–14)
Though it is clear that neutrinos do contribute to the total energy content of the universe,
they cannot account for the dark matter.
1.3.2 Axions
The axion is a pseudo-Nambu-Goldstone boson that results from the hypothetical
Peccei-Quinn symmetry. A QCD phase change in the early universe spoiled this symmetry,
giving the axion a small mass. This particle was originally proposed as a mechanism to
restore CP-symmetry in QCD [26] after ’tHooft showed that strong interactions possess an
unbounded parameter θ allowing CP-violation.
Axions could have been produced in cosmologically-interesting amounts in the early
universe by a variety of mechanisms, the favored being vacuum misalignment [27]. This
29
mechanism yields a relic density given by [28],
Ωa ∼(
5 µeV
ma
)7/6
. (1–15)
The axion’s mass, ma, is given by,
ma ∼ 6 µeV
(1012 GeV
fa
), (1–16)
where fa is the energy scale at which the Peccei-Quinn symmetry is broken. The mass
is constrained to lie in the range 10−6 eV . ma . 10−3 eV; the lower bound arises to
prevent the axion from over-closing the universe, while the upper bound is enforced from
measurements of SN1987A. The argument for the lower bound is obvious from equation
1–15, because Ωa grows as ma decreases. The upper bound from Sn1987a comes from
the fact that if the axion’s couplings (proportional to ma) are too great, it would allow
significant cooling during the supernova and would be observable.
Figure 1-7. The parameter space typically used for axion searches, axion-photon couplingversus axion mass. The mass range allowed for interesting cosmologicalconsequences is 10−6 eV . ma . 10−3 eV. Axion dark matter searches arethose label “microwave cavity”. Figure taken from [28].
30
The current experiments searching for dark matter axions attempt to stimulate the
decay of an axion into a single radio-wavelength photon [27]. The experiments utilize radio
resonance cavities with tunable resonance frequencies, with applied static magnetic fields.
The standard axion parameter space, along with the results of recent searches, is shown in
Figure 1-7.
1.3.3 Thermal Freeze-Out and the Weakly Interacting Massive Particle
The axion of the previous section, while an excellent solution to the strong CP
problem, requires some specific conditions for it to be cosmologically important.
In particular, the axion’s small mass requires that it was produced out of thermal
equilibrium. In contrast, one can explore the possibilities of dark matter candidates
that originate as thermal relics, a process known as thermal freeze-out.
Shortly after the Big Bang, a particle species is in thermal equilibrium with the
rest of the universe if its production rate and annihilation rate are equal. As time
progresses, these rates begin to differ, the nature of which depends upon the particle’s
annihilation cross section and mass. Once the temperature of the universe falls below the
production threshold of this species, production ceases. Additionally, the expansion of
the universe suppresses the annihilation rate; if this rate drops below the expansion rate
then annihilation ceases as well, and a relic density of this particle will remain. The relic
density of particle X depends upon 〈σv〉 as [29]:
ΩXh2 =mXnX
ρc
h2 ≈ 3× 10−27 cm3 s−1
〈σv〉 (1–17)
where mX , is the WIMP mass, nX is the number density, and 〈σv〉 is the thermally
averaged total annihilation cross section multiplied by the velocity. In order for ΩX to
have a value close to what we observe today, X must have a weak cross section [30], which
already rules out most of the particles in the Standard Model.
As discussed with relic neutrinos in section 1.3.1, a “hot” (i.e. relativistic) dark
matter candidate would destroy the formation of large-scale structure. While the density
31
of thermal relic X depends only weakly on its mass, the temperature at which it freezes
out depends on the mass as T ' mX/20 [23, 29]. This places a lower limit on the mass
at ∼10 keV. However, the fact that such a particle has not been seen in colliders like LEP
increases the lower limit to ∼30GeV [29]. Given these properties, that such a particle must
have a weak cross section and large mass, this type of dark matter candidate is typically
called a Weakly Interacting Massive Particle, or WIMP.
In addition to a lower limit on the mass, an upper limit can be inferred. Based on the
so-called unitarity bound, which implies a relationship between a particle’s mass and it’s
maximum possible annihilation cross section, cosmological measurements constrain that
mX is less than ∼34TeV [7].
axion axino
neutrino
WIMP
gravitino
Mass [GeV c−2]
σ int [c
m2 ]
XENON10
10−15
10−10
10−5
100
105
10−80
10−70
10−60
10−50
10−40
Figure 1-8. A survey of the σ versus mass parameter space for various particle dark mattercandidates. The solid black line is the upper limit from the XENON10 WIMPsearch [31]. Figure adapted from [32].
The power of the thermal freeze-out mechanism is that it is model independent.
It requires only that nature simply allows for the existence of a particle with those
properties; the specifics of the model do not come into the calculation of equation 1–17. It
is also a fact that any new physics beyond the Standard Model (BSM) almost generically
produces a particle with these properties. Existing results of collider experiments can be
used to make an indirect estimate of the Higgs boson mass, at mH = 129+74−49 GeV/c2[20].
32
New physics at or below the ∼TeV scale is necessary to cancel quadratically diverging
radiative contributions to the Higgs mass. A new particle at the electroweak scale will
already have the required annihilation cross section, because σ ∼ α2/M2 [33], where
α is the weak coupling constant. Additionally, new particles at the TeV scale would
significantly alter the results of precision studies of electroweak physics, and thus a
conservation law must be invoked that allows only even numbers of BSM particles at
interaction vertices, for BSM particles up to ∼5-7TeV [34]. Such a conservation law
would force the lightest of such BSM particles to be stable. Figure 1-8 shows various
particle dark matter candidates, along with the XENON10 WIMP search exclusion
limit [31]. Popular WIMP candidates are the neutralino from supersymmetry, the LKP
from universal extra dimensions, and the little Higgs model.
In the Minimal Supersymmetric Standard Model (MSSM), the superpartners of the
standard model gauge bosons mix into two charged mass eigenstates called charginos, χ±1,2,
and four neutral eigenstates called neutralinos, χ01,2,3,4 [7]. In many scenarios, the lightest
supersymmetric particle is χ01. Various theoretical arguments suggest that there is an
additional symmetry called R-parity, the leads to the conservation of R ≡ (−1)2s+3B+L,
where s is the spin, B is the baryon number, and L is the lepton number. Therefore
Standard Model particles have R = 1 and all superpartners have R = −1; the lightest
supersymmetric particle would then be stable.
Theories that explore the possibility of the existence of more than 3+1 dimensions
are called Kaluza-Klein theories. The extra dimensions must in some way be compactified,
meaning they are wrapped up on some small size, explaining why we do not experience
them. The momentum of fields propagating in these extra compactified dimensions
thus becomes quantized. All Standard Model particles exhibit the lowest momentum
mode in the extra dimensions, and excitations have an increased mass according to
mn ∝ n/R, where n is the excited mode (Standard Model particles have n = 0), and
R is the size characterizing the scale of compactification. Conservation of momentum in
33
the extra dimensions leads to a symmetry called KK-parity, which essentially conserves
mode number. In universal extra dimensions, the first excitation of the B boson, B(1), is
typically the lightest of all the n = 1 excitations (LKP), and is therefore stable.
The little Higgs models posit that the Higgs doublet is actually a massless Nambu-
-Goldstone boson, but due to a break in symmetry carried by its couplings, it becomes a
massive pseudo-Nambu-Goldstone boson. The symmetry is only broken in the presence of
more than one set of couplings, and therefore the Higgs mass does not receive diverging
contributions at the one-loop level [34]. Little Higgs models generically contain new
particles at the TeV scale which could account for the dark matter.
34
CHAPTER 2DIRECT DETECTION AND LIQUID XENON
Hell would be a small universe that wecould explore thoroughly and fully comprehend.
-Timothy Ferris
In the previous chapter, evidence for the existence of dark matter on the scale of
galaxies was discussed (Section 1.2.1). While many dark matter candidates have been
proposed, with varying degrees of justification, none of the existing observations can tell us
much more about dark matter’s identity.
In order to learn more, the dark matter must be unambiguously detected, or the
products of its decay, annihilation, or co-annihilation must be detected. The latter, known
as indirect detection, has been offered, for example, as a possible explanation for the
excess of 511 keV γ-rays coming from the center of the Milky Way [35]. The former, known
as direct detection, aims to observe WIMPs interacting with normal matter. The basics of
direct detection, the most sensitive examples of existing experimental efforts, the benefits
of liquid xenon (LXe), and finally, the physics of particle interactions in LXe are discussed
in the present chapter.
2.1 The Local Dark Matter Environment
There is some debate as to the exact distribution of dark matter galaxy halos,
however, all halo profiles share more or less the same general features outside of
the galactic bulge. Estimates of the local dark matter density are made based on
measurements of the rotational velocity of the sun and nearby stars around the Milky
Way. While this measurement gives only the total mass residing inside our solar radius,
the actual density can be inferred by combining these measurements with various halo
parameterizations taken from N-body simulations [7].
These techniques estimate the local dark matter density to lie somewhere in the range
0.2 . ρ0 . 0.6 GeV c−2 cm−3, with the preferred value being ρ0 = 0.3GeV c−2 cm−3, a
characteristic average velocity of v = 230 km s−1 and escape velocity of 600 km s−1 [7, 29].
35
As our solar system orbits the center of the Milky Way, it is essentially traveling
through a diffuse gas of weakly interacting particles with the kinematic properties
described above. The rotational velocity of the sun in its galactic orbit is typically
taken to be 244 km s−1, with the Earth’s motion around the sun providing a sinusoidal
oscillation in this velocity at the level of 15 km s−1 [36]. Though feeble, WIMPs passing
through the Earth should occasionally interact with normal matter. The energy transfered
in these interactions is expected to be small, but nonetheless detectable given a particle
detector with the appropriate properties.
2.2 WIMP Interaction Rates
When interacting with normal, atomic matter, WIMPs will primarily interact with
the atomic nuclei, rather than with electrons. For WIMPs passing at a fixed velocity, v,
through a target of a single atomic species, the interaction rate, in events per unit target
mass, is given by,
R ≈ ρ0σv
mχmN
, (2–1)
where ρ0 is the mass density of WIMPs, σ is the elastic scattering cross section, and mχ
and mN are the masses of the WIMP and nucleus, respectively. This picture is, however,
too simple to be useful in this form, for two reasons. First, though the picture painted in
the previous section is that of an Earth flying through a gas of WIMPs at ∼244 km s−1,
the velocity of the WIMPs themselves is far from uniform, and hence the WIMP velocity
dispersion must be taken into account. This is done by replacing the velocity, v, by a
kinematic form factor, T (Q), where Q is the energy transfer, that is weighted according
to the allowed velocities. Second, the elastic scattering cross section, σ, is not uniform
with energy, and must instead be replaced by σ → σ0F2(Q), where σ0 is the cross section
in the limit of zero energy-transfer, and F 2(Q) is the nuclear form factor, characterizing
how the cross section evolves with energy. Combining these modifications gives the total
36
differential cross section as [29],
dR
dQ=
ρ0σ0√πv0mχm2
r
F 2(Q)T (Q) (2–2)
where mr is the reduced mass of the WIMP-nucleus system and v0 is the characteristic
WIMP velocity. T (Q) must take into account not only the velocity of the Earth and Sun
and the velocity dispersion of the WIMPs, but also the galactic escape velocity. It is given
by [36],
T (Q) = kv0
√π
4ve
erf
(vmin + ve
v0
)− erf
(vmin − ve
v0
)− exp
[−
(vesc
v0
)2]
(2–3)
where ve is the (Sun and Earth)’s velocity, vesc is the galactic escape velocity, vmin is the
minimum velocity that a WIMP must have in order to produce a recoil of energy Q,
vmin =√
QmN/(2m2r), and the prefactor k is given by,
k = erf
(vesc
v0
)− 2vesc
v0πexp
[−
(vesc
v0
)2]
. (2–4)
From here, there remain two pieces of Equation 2–2 unaddressed: σ0 and F 2(Q).
These depend on the type of interaction that governs the WIMP-nucleus scatter, and
cannot be solved in the general sense. At the low values of Q that typically characterize
direct searches, the two types of interactions of importance are scalar (spin-independent)
and axial-vector (spin-dependent) [7].
2.2.1 Spin-Independent Interactions
In the case of scalar interactions, spin-independent (SI), the WIMP-nucleus
interaction is typically assumed to make no distinction between protons and neutrons,
and instead only considers the number and spatial distribution of the nucleons. The
Woods-Saxon form factor describes the spatial extent of the nucleus [29], and is given by,
F (Q) =3j1(qR)
qRe−(qs)2/2, (2–5)
37
where q =√
2mNQ is the momentum transfer, s ' 1 fm, R '√
1.44 fm2A2/3 − 5s2, and
j1(qR) is the n = 1 spherical Bessel function of the first kind. The cross section as Q → 0,
σ0, is given by,
σ0(Z,A) =4m2
r
π[Zfp + (A− Z)fn]
2 ' 4m2r
πA2f 2, (2–6)
where Z is the atomic number, A is the mass number, and fp(n) is the WIMP SI coupling
to protons (neutrons). As previously stated, SI interactions are typically taken to be
isospin-invariant, and hence the proton and neutron couplings are assumed to be identical,
fp = fn = f . Nevertheless, f is left undetermined and must be calculated based on a
particular particle physics model. Because of this, the cross section is usually normalized
to the WIMP-nucleon cross section, as,
σ0(A)
σ0(1)=
(mr
mn
)2
A2, (2–7)
where mn is the WIMP-nucleon reduced mass. The cross section is now in a form that
is not only model-independent, but facilitates easy comparison between various detector
materials. The expected SI differential scattering rates for three nuclei are shown in Figure
2-1. The advantage given to Xe (A=131) by the scaling of σ0 with A2 is evident at low
energies, demonstrating one advantage that this nucleus has for direct detection.
2.2.2 Spin-Dependent Interactions
Unlike the relatively straight-forward case of SI interactions, the spin-dependent (SD)
interactions are quite complex. We again start with the two undetermined parameters, σ0
and F (Q), from Equation 2–2. However, because the WIMPs couple to the nuclear spin,
the detailed structure of the nucleus must be considered. Additionally, unlike the SI case
where it was reasonable to take the proton and neutron couplings as being identical, here
we cannot make such an assumption.
The SD cross section at zero-momentum transfer is given as [29],
σ0 =32
π4G2
F m2r[ap〈Sp〉+ an〈Sn〉]2
(J + 1
J
), (2–8)
38
Recoil Energy [keV]
Diff
eren
tial R
ate
[kg−
1 day
−1 k
eV−
1 ]
0 20 40 60 80 10010
−6
10−5
10−4
10−3
Ar A=40Ge A=73Xe A=131
Figure 2-1. The expected spin-independent differential recoil spectra in Ar, Ge, and Xe ofa WIMP of mass 100GeV c−2, and a cross section with nucleons of1× 10−44 cm2
where GF is Fermi’s constant, J is the spin of the nucleus, ap(n) is the SD coupling of
WIMPs to protons (neutrons), and 〈Sp(n)〉 is the spin content of the protons (neutrons)
in the nucleus. As a first approximation it is valid to assume that the entire spin of the
nucleus is carried by the un-paired nucleon. However, precise calculations of the spin
content of most nuclei indicate that even the fully-paired nucleons contribute at least a
small amount to the total nuclear spin. This will be discussed more in Section 3.3.2.
Because the proton and neutron couplings are unequal, the cross section cannot be
normalized to the WIMP-nucleon cross section. Instead, the normalization is performed
by considering if the WIMPs were to only couple to protons (i.e. an = 0) and then
normalizing to the WIMP-proton cross section, as
σ0(an = 0)
σ0(proton)=
4
3
(mr
mp
〈Sp〉)2 (
J + 1
J
), (2–9)
where mp is the WIMP-proton reduced mass. The converse normalization is likewise
made, by assuming that the WIMPs only couple to neutrons (i.e. ap = 0) and normalizing
to the WIMP-neutron cross section. Here again the coupling constant has been divided
out and we are left with an expression that is model-independent.
39
The SD nuclear form factor also is more complicated than in the SI case. F 2(Q) is
written as the normalized spin form factor given by F 2(Q) = S(|q|)/S(0). Unlike the SI
case, here the spin form factor depends on the SD couplings as,
S(q) = a20S00(q) + a2
1S11(q) + a0a1S01(q), (2–10)
where q is the momentum transfer, a0 = ap + an, a1 = ap − an, and the Sij(q) describe how
the spin is spatially distributed within the nucleus, and must be taken from models of the
nuclear spin structure.
2.3 Direct Detection Strategies
The expected behavior of WIMP interactions with normal matter define specific
strategies for pursuing a direct detection. The fact that WIMPs will interact primarily
with atomic nuclei is important, because the backgrounds in low-energy particle detectors
are predominantly electromagnetic in origin. It is therefore desirable to develop a detector
technology that is capable of distinguishing between the two types of interactions.
Sensitivity to SD interactions stipulates detector media with nonzero nuclear spin.
SI interactions, whose rate is proportional to A2 (Equation 2–6), demand detector
materials with large nuclei. The low expected event rate (Figure 2-1) requires a detector
with a large overall target mass. Several direct detection experiments following these
requirements, which have the current best sensitivities, are discussed in this section,
finishing with a discussion of what LXe has to offer the field.
2.3.1 Examples of Direct Detection Experiments
The two experiments with the current best sensitivity for SI and pure-neutron SD
interactions are XENON10 [31] (the focus of Chapter 3) and CDMS-II [37]. The physics
underlying the techniques that both detectors use in order to distinguish electronic from
nuclear recoils, nuclear recoil discrimination, are similar. That is, both experiments make
use of parameters related to the ionization yield, or the amount of ionization collected for
a given energy. The process of nuclear recoil discrimination in the XENON10 experiment
40
is discussed in detail in Section 3.1.3. The ionization yield is employed because nuclear
recoils produce a higher ionization density than electronic recoils, and hence lead to
stronger electron-ion recombination following an interaction.
The CDMS-II experiment uses an array of germanium and silicon detectors cooled
to tens of mK. The detectors measure energy deposition simultaneously in the form
of athermal ballistic phonons and ionization. The ionization yield of the interaction is
taken from the ratio of the two signals, shown in Figure 2-2. As expected, the stronger
electron-ion recombination of nuclear recoils results in a suppressed ionization yield
compared to electronic recoils.
0 20 40 60 80 1000
0.5
1
1.5
Recoil Energy (keV)
Ioni
zatio
n Y
ield
Figure 2-2. Ionization yield versus energy in the CDMS-II experiment from calibrationsources. Electronic recoils are in blue, nuclear recoils in green. Solid anddashed lines correspond to the ±2σ bounds of the electronic and nuclear recoilbands, respectively. Figure taken from [38].
The current two strongest limits on pure-proton SD interactions come from the
KIMS [39] and COUPP [40]. The two experiments use vastly different techniques, but
share their exceptional sensitivity to pure-proton SD interactions due to the high proton
content of their nuclear spins.
41
The KIMS experiment [39] uses an array of CsI(Tl) scintillating crystals, held at
T = 0 C. This experiment makes use of the fact that the scintillation emission time scale
for electronic and nuclear recoils is statistically different, which results from the differing
linear energy transfer (LET) of the two species. A distribution function characterizing the
arrival time of photoelectrons from the photomultiplier tubes, f(t), is constructed, and is
then used to find the mean time (MT ) of an event from MT =∫
tf(t)dt/∫
f(t)dt. The
distributions of MT for electronic and nuclear recoil calibration data are shown in Figure
2-3. Given the relative overlap of the two signals, nuclear recoil discrimination must be
performed on a statistical bases, rather than an event-by-event basis as in the CDMS-II
and XENON10 experiments.
sec)µMean Time (1
Eve
nts
1
10
210
30.4
Figure 2-3. Distributions of the discrimination parameter, mean time, from one crystalused in the KIMS experiment. Open squares are from nuclear recoil calibrationdata, open circles from electronic recoil calibration, and closed triangles fromWIMP search data. Plot taken from [39].
The COUPP experiment [40] uses a superheated CF3I liquid bubble chamber held
at close to room temperature, and images the liquid with high-speed cameras searching
for the creation of bubbles. Bubbles nucleate from regions of ionized liquid and grow
to macroscopic sizes. The power of this technique is that by tuning the pressure and
temperature, the threshold for bubble nucleation can be adjusted. These thermodynamic
parameters are set so that the relatively low ionization density of electronic recoils
42
is unable to form bubbles, while allowing bubble formation from the much higher
ionization density arising in nuclear recoils. Examples from three classes of bubble-creating
interactions are shown in Figure 2-4. The actual total energy of an interaction cannot be
determined, however, and instead an integrated rate is observed. The spectrum of recoil
energies is probed by collecting data sets with varied energy thresholds.
Figure 2-4. Examples of three classes of particle interactions in the COUPP bubblechamber. Photographs correspond to (A) cosmic rays, (B) neutrons, and (C)WIMP-like interactions. Figure taken from [40].
2.3.2 Why Liquid Xenon?
LXe, the focus of this dissertation, has a wide variety of properties deemed useful in
a direct detection search for WIMPs. With an atomic weight of 131.3 gmol−1, its nuclei
present a large target sensitive to SI interactions, whose cross section scales roughly with
A2 (Equation 2–6). Additionally, nearly half of its naturally occurring isotopes carry spin,
presenting sensitivity to SD interactions.
Despite the ability to reject electronic recoils in LXe (see Section 3.1.3), background
events must nonetheless be minimized. LXe offers several features that help to facilitate
this effort. First, there exist no long-lived naturally occurring xenon radioisotopes (unlike
Ar which suffers from 39Ar), and hence there are no intrinsic background sources at the
interior of a LXe detector. Additionally, xenon is a formidable absorber of γ-rays due to
its high Z. Given a sufficiently large detector volume, the outer regions of the detector
43
volume absorb much of the background γ-rays, leaving the inner regions with a highly
reduced γ background. This property is known as self shielding.
LXe presents a relatively straightforward path towards scalability of detector mass,
compared to other detector technologies discussed here. This is because the technical
challenges involved in scaling a liquid tank by a factor of ten are trivial compared with
the challenges of trying to grow a crystal ten times larger. There are two advantages to
scaling up the detector’s mass. First, the expected WIMP interaction rate scales linearly
with the target mass, providing a run time incentive for detector scalability. Second,
larger detectors provide more effective self shielding than smaller ones. The combination
of these two features means that as the detector mass is scaled up, the expected signal
rate increases, while simultaneously the background rate decreases; both effects boost the
overall sensitivity.
2.4 Liquid Xenon Interaction Physics
2.4.1 Microscopic Processes in a Particle Track
A recoiling particle in LXe leaves behind a track of electrically neutral, excited xenon
atoms (‘excitons’) and positively-charged ionized xenon atoms (‘ions’). The processes
occurring after these ions and excitons are created are what lead to the scintillation and
ionization signals that are used for particle detection.
Figure 2-5 shows the potential energy of electronically excited Ar atoms in the
vicinity of ground-state Ar atoms, as a function of separation. Though two ground-state
argon atoms are strongly repulsive at short distances, Ar∗+Ar and Ar++Ar see potential
wells that form bound states, called self-trapped excitons and ions, respectively. This
energy scheme is characteristic of rare gases, including xenon. An ionized xenon atom can
go through a process of dimer formation and electron recombination that leads to a singly
44
Figure 2-5. Potential energy curves of ground-state argon in proximity to excited orionized argon atoms. The main component of the scintillation spectrum comesfrom the transition labeled ‘II’. Figure taken from [41].
excited xenon atom [42]:
Xe+ + Xe → Xe+2
Xe+2 + e− → Xe∗∗ + Xe
Xe∗∗ → Xe∗ + heat , (2–11)
where the superscripts +, *, and ** indicate singly ionized, singly excited, and doubly
excited atoms, respectively. For some of the ions in a recoil track, this process can be
halted at the second line of Equation 2–11. This can happen either because the electron
has been carried away by thermal motion, or because it has migrated away from the track
under the influence of an applied electric field. The latter case leads to a cloud of drifting
electrons that can be read out as an ionization signal. The positive ions that result from
45
incomplete electron recombination drift to the cathode, but at a rate that is three to five
orders of magnitude smaller than the electron drift velocity [43]. The final state Xe∗ atom
is in the same state as those neutral atoms in the track that experience only electronic
excitation. These excitons relax to ground-state atoms in a similar process:
Xe∗ + Xe → Xe∗2
Xe∗2 → 2Xe + hν (2–12)
The final step of Equation 2–12 corresponds to the the transition in Figure 2-5 labeled ‘II’,
releasing 7.0 eV. This corresponds to the peak in the scintillation spectrum of 178 nm, with
a width of 13 nm [44].
For regions of high excitation density, it can be possible for two excitons to interact
directly, before becoming self-trapped, in the process,
Xe∗ + Xe∗ → Xe + Xe+ + e−. (2–13)
This process converts two excitons into a neutral and singly-ionized atom, and acts to
quench the overall particle signal: the two excitons which might normally each produce
a scintillation photon are now replaced by a single ion, capable of yielding at most one
photon. As this process requires excitons interacting directly, it is expected to play
significant roles in only those recoil tracks with the highest excitonic densities: nuclear
recoils, alpha particles, and fission fragments [45].
2.4.2 Lindhard Quenching
In situations where the projectile particle and the target particles are of comparable
mass, low energy projectiles can often lose a significant amount of their energy through
elastic collisions that add heat to the target but do not electrically excite or ionize a
target atom. Such a collision involves energy transfer that is completely emissionless,
and therefore the energy reconstructed based on scintillation and charge collection
underestimates the true energy of the projectile. Energy loss from these emissionless
46
collisions is known as nuclear stopping,1 while energy loss via collisions that produce
electronic excitation is known as electronic stopping.
The ratio of energy lost in electronic stopping to the total energy loss is given by the
Lindhard factor, fn [36]. In the case of WIMP scatters, the relevant interactions are Xe
recoils in Xe; when the target and the projectile are identical, as in this case, fn is given
by [46],
fn =kg(ε)
1 + kg(ε), (2–14)
where k a dimensionless constant characterizing the nuclear size and charge, ε is a function
of the recoil energy and Z, and g(ε) is an algebraic function of ε. These three quantities
are determined empirically and can be found in [36].
2.4.3 Putting it All Together: Leff
From Sections 2.4.1 and 2.4.2, it is clear that the connection between the total
energy of a projectile, and the number of collected scintillation photons, is not so direct.
Energy can be lost via electrons escaping recombination (Equation 2–11), biexcitonic
quenching (Equation 2–13), and Lindhard quenching (Equation 2–14). Furthermore,
the amount of energy that is lost in each of these three effects depends on the identity
of the recoiling particle. Because of this, the unit of energy assigned to an event carries
a suffix that designates the type of recoiling particle. The unit ‘keVee’ stands for ‘keV
electron-equivalent’, meaning the number of scintillation photons acquired is equivalent to
the number that would be emitted by a recoiling electron of that energy. The unit ‘keVr’
indicates ‘keV nuclear recoil equivalent’, and similarly indicates the amount of collected
scintillation light is equivalent to what would be emitted from a recoiling Xe nucleus of
that energy.
1 “Nuclear stopping” is a bit of a misnomer because the collisions involve the entireatom as whole, not just the nucleus.
47
One must therefore have a method of understanding the energy deposition from an
unknown particle (WIMP→Xe recoil), given a calibration with a known source (γ-ray→e−
recoil). Such a calibration sets an energy scale for a detector, known as the yield. The
yield is generally given in quanta/keV, where ‘quanta’ can mean photons, electrons, or
photoelectrons. The ratio of the yield from nuclear recoils to yield from a calibration
source (typically 57Co for LXe detectors) is known as Leff . This energy dependent quantity
has been extensively studied both theoretically, by Hitachi [45], and experimentally by
various groups [47–53], and is the focus of Chapter 4.
48
CHAPTER 3THE XENON10 EXPERIMENT
The world is a book and those who do not travel only read one page.
-Saint Augustine
3.1 The XENON10 Detector and Underground Facility
3.1.1 Detector Description
The XENON10 detector is a 3-D position sensitive dual phase (liquid-gas) xenon
Time Projection Chamber (TPC), seen in Figure 3-1. The active volume is 20 cm in
diameter and 15 cm in height, defined on the perimeter by a hollow polytetrafluoroethylene
(PTFE) cylinder and on top and bottom by mesh electrodes. The cathode mesh electrode
at the bottom and the gate mesh at the top define a downward electric field, Ed, of
0.73 kV cm−1; 5 mm above the gate mesh is the anode mesh, with the liquid level lying
between the gate and anode. A fourth mesh, 5 mm above the anode, is held at the same
potential as the gate, and serves to prevent any extracted electrons from escaping the
anode. After fiducial cuts, the mass of LXe used for the WIMP search is 5.4 kg. The
temperature is kept constant at 180K, cooling provided by a pulse tube refrigerator
(PTR).
An array of 47 photomultiplier tubes (PMTs) view the volume from the top, in the
gas. A second array of 41 PMTs views the active volume from below, lying below the
cathode mesh. Following a particle interaction, the excitons and recombining electrons
produce scintillation light within tens of nanoseconds. The electrons that escape
recombination are drifted up to the liquid surface by Ed and into the gas, where they
produce secondary scintillation light as they collide with gaseous xenon atoms during their
transit towards the anode. In this way both prompt scintillation (S1) and ionization (S2)
signals can be measured simultaneously with the PMTs.
The position of an event is determined by the characteristics of the S2 signal. Seen
in Figure 3-2, the drift velocity of electrons in liquid xenon is well known as a function
49
Vacuum
electrodesMesh
PMTs
LXePTFE
PTR GXe
Figure 3-1. Schematic of the XENON10 detector. The active LXe detector is defined ontop and bottom by mesh electrodes, and on the perimeter by a PTFE cylinder.Cooling is provided by the PTR at the top-left.
of applied field. The delay time between S1 and S2 thus gives the transit time of the
electrons, and therefore the z-position of the event with 1 mm resolution. Because the S2
scintillation light is emitted in the gas gap, 1 cm below the top PMT array, this signal
will be highly localized in the PMTs lie directly above the interaction site. In order to
obtain a precise reconstruction of the x-y position, a Monte Carlo (MC) simulation is used
to estimate the expected PMT hit pattern given a S2 position. An evenly spaced grid of
points in x-y is selected, and for each point in the grid the PMT hit pattern estimated.
This MC hit map is then used to train a neural network in reconstructing the x-y position
from a measured signal pattern on the top PMT array, with precision to within a few
millimeters.
50
Figure 3-2. The drift velocity of electrons in xenon as a function of applied electric field.Figure taken from [54].
Calibration of XENON10 is done with a variety of sources, each for a different
purpose. The S1-based energy scale, determined by 122 keV γ-rays from 57Co, is found to
give a volume-averaged light yield of 3.0±0.1(sys)±0.1(stat) p.e./keVee. The response of
the detector, like all detectors, varies depending on the location of the event vertex. In
order to measure these variations, 131mXe was introduced, providing a spatially-uniform
source of 164 keV γ-rays and conversion electrons. The low-energy response to electronic
recoils was measured with 662 keV gamma rays from 137Cs undergoing Compton scatters
within the active LXe volume. Similarly, the low-energy nuclear recoil response was
measured with multi-MeV neutrons from a AmBe source. These two calibrations are
discussed in Section 3.1.3.
3.1.2 Laboratori Nazionali del Gran Sasso
The XENON10 experiment was operated at the Laboratori Nazionali del Gran Sasso
(LNGS), an underground physics facility located in Abruzzo, Italy. It provides roughly
3.1 km water equivalent (km.w.e.) shielding against cosmic rays, reducing the flux of
cosmic ray muons by a factor of roughly 5 × 10−7 compared to the rate at the surface [55].
An existing 10 km underground highway tunnel provides access to the laboratory, which
51
consists of three main caverns (Halls A, B, and C) and peripheral service tunnels, also
outfitted for experiments. The layout of these can be seen in Figure 3-3.
Figure 3-3. The layout of the underground LNGS facility.
The detector and cryostat were located inside a specially designed shield, providing
20 cm of lead and 20 cm of high-density polyethylene (HDPE). The lead shield acts to
attenuate external electromagnetic backgrounds, while the HDPE slows neutrons. The
detector can be seen in the opened shield in Figure 3-4. The visible part of the shield is
the door; under normal operation the door is closed and the cavity housing the detector is
flushed with boil-off nitrogen gas in order to purge the volume of radon.
3.1.3 Nuclear Recoil Discrimination
The success of XENON10 as a dark matter detector in large part hinges upon its
ability to discriminate electronic recoils from nuclear recoils, which in turn requires
adequate definition of the detector responses to such events based on calibration data.
This technique is called nuclear recoil discrimination. In addition to excitons, any
recoiling particle will produce a population of ionized electrons, many of which promptly
recombine with their parent ions. As Ed is increased, the relative number of recombining
electrons decreases. However, because nuclear recoil tracks have a characteristically higher
52
Figure 3-4. The XENON10 detector seen inside the lead and HDPE shield.
ionization density than electronic recoils [56], fewer electrons escape recombination from
recoiling nuclei than electrons for a given energy and Ed.
Electrons that recombine contribute to the prompt scintillation signal (S1), while
those escaping recombination are drifted to the anode in the gas and produce the
proportional signal (S2). Therefore, the relative strength of recombination for a given
event can be measured by the ratio S2/S1, and hence this parameter can be used to
discriminate between recoiling species. Figure 3-5 shows the behavior of log10(S2/S1) as
a function of energy for populations of both recoil types, called the electronic and nuclear
recoil bands, or ER and NR bands, respectively. The main purpose of such calibrations
is to identify a region in log10(S2/S1)–S1 space, called the WIMP acceptance window,
which should be nearly free of ER events while covering a significant portion of the
NR band. The lower bound of this window along the horizontal axis is determined by
the detector’s S1 threshold. The corresponding upper bound is chosen to maximize the
potential integrated WIMP rate while minimizing the effects of ‘gamma-x’ events which
53
occur mostly at higher energies. These events are multiple-scatter events with only one
event vertex residing in the active region, and are therefore reconstructed as single scatters
with anomalously low log10(S2/S1) values. The choice of bounds along the vertical axis is
discussed here.
S1 [keVee] (2.2 p.e./keVee)
log 10
(S2/
S1)
0 2 4 6 8 10 12 14 16 18 200.5
1
1.5
2
2.5
3
3.5
137Cs (662 keV gamma)AmBe (neutron)
Figure 3-5. The electronic and nuclear recoil bands shown in log10(S2/S1) versus S1 space.
The calibration of the ER band is performed using a 2 µCi 137Cs source that emits a
662 keV γ-ray, placed outside the cryostat and PTFE shield but inside the lead shield. The
attenuation length of 662 keV γ-rays in LXe is roughly 4.5 cm, which means these photons
are able to reach all regions of the r = 10 cm detector given sufficient exposure. Data
were taken with this source throughout most of November 2006, and intermittently from
December 1 through February 14 2007, accumulating a total of ∼2100 events (after quality
and fiducial cuts) in the WIMP acceptance window’s S1 range, 4.4 p.e.≤ S1≤ 26.4 p.e.
Fluctuations in log10(S2/S1) over most of this range are dominated by recombination
fluctuations, until the lowest energies where uncorrelated statistical fluctuations take over.
The width of the ER band is very important in regards to nuclear recoil discrimination
because it partially overlaps with the NR band. Due mainly to the non-uniform S1
response at different locations within the active region, performing spatially-dependent
corrections to S1 based on the 131mXe calibration improves the overall S1 resolution and
thus helps to reduce the variance of the bands (the superscript ‘m’ following the atomic
54
number denotes a metastable nucleus). A 100 µCi AmBe source (220 ± 15%n s−1) is used
for the definition of the NR band. Data were acquired with the source on December 1,
2006 for approximately 12 live-hours.
The energy dependence of both bands makes it difficult to measure precisely the
discrimination power in the absence of extraordinarily large calibration datasets. In an
effort to remove this energy-dependence, a one-dimensional transformation that “flattens”
the ER band is applied to all data. The ER band is broken up into 1 keVee-wide, vertical
slices in S1. For each, a Gaussian fit is applied to the log10(S2/S1) spectrum. The mean of
each fit now represents the center of the ER band in that particular bin. A polynomial is
fit to the Gauss means, providing an analytic form for the ER band centroid as a function
of S1, and is subtracted from every data point in both bands. This procedure removes the
energy dependence of the ER centroid (and to a large extent, the NR centroid as well),
and introduces a new parameter, ∆ log10(S2/S1), representing the distance from the ER
centroid in log10(S2/S1) space. Figure 3-6 shows the bands in ∆ log10(S2/S1) space.
S1 [keVee] (2.2 p.e./keVee)
∆ lo
g 10(S
2/S
1)
0 2 4 6 8 10 12 14 16 18 20−1.5
−1
−0.5
0
0.5
1
137Cs (662 keV gamma)AmBe (neutron)WIMP ROI
Figure 3-6. The bands in Figure 3-5 have been transformed to show the distance inlog10(S2/S1) space from the ER band center, giving the new discriminationparameter, ∆log10(S2/S1). The vertical lines indicate the WIMP region ofinterest (ROI).
Although the energy dependence of the ER band centroid has been removed, the
NR band centroid and width still exhibit energy dependence. The flattened bands are
55
again broken up into vertical S1 slices, only this time more coarse binning is used–seven
bins in the WIMP energy range–in order to maximize the statistics in each slice, and
a Gauss fit is applied to the ∆log10(S2/S1) spectrum of both bands. One such slice
is shown in Figure 3-7. The WIMP acceptance window is defined to lie in the range
(µ− 3σ) < ∆log10(S2/S1) < µ, where µ and σ are the mean and sigma from the NR band
Gauss fits, respectively. The Gauss fits are performed only to define the window bounds;
the NR acceptance, Anr, is calculated by counting the fraction of AmBe events that fall
within this window, for each energy bin.
∆ log10
(S2/S1)
Cou
nts
(a)
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.60
5
10
15
20
25
30
∆ log10
(S2/S1)
Cou
nts
(b)
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.60
10
20
30
40
50
60
Figure 3-7. Distributions of ∆log10(S2/S1) for nuclear (black) and electronic (red) recoilsin the range (a) 4.5–6.7, and (b) 13.4–17.9 keVr. The black histogram in (a)has been scaled down by a factor of 4. The WIMP acceptance window in thisparticular energy range is defined by the blue, shaded rectangle which isbetween µ and µ− 3σ of the NR band.
The shape of the ∆log10(S2/S1) fluctuations in the ER band are “empirically”
Gaussian; that is, they appear consistent with a Gaussian distribution given the available
statistics. As previously stated, the width of the ∆ log10(S2/S1) spectrum is dominated
by recombination fluctuations, which are poorly understood, and thus more cannot be
said from an empirical standpoint in the absence of a larger calibration dataset. An
attempt to study the band shape with a Monte Carlo simulation is discussed in Section
3.2. The predicted ER rejection is calculated in the case that ∆log10(S2/S1) fluctuations
are Gaussian. That is, the Gauss fits to the ∆log10(S2/S1) spectrum in each of the seven
56
Table 3-1. The nuclear recoil acceptance, Anr, and the electron recoil rejection efficiency,Rer, for each of the seven energy bins. The predicted number of leakage events,Nleak, is based on Rer and the number of background events, Nevt, in eachenergy bin, for the 58.6 live-days WIMP-search data. Errors are the statisticaluncertainty from the Gaussian fits on the electron recoil ∆ log10(S2/S1)distribution.
Enr (keV) Anr 1 - Rer(10−3) Nevt Nleak
4.5 - 6.7 0.446 0.8+0.7−0.4 213 0.2+0.2
−0.1
6.7 - 9.0 0.458 1.7+1.6−0.9 195 0.3+0.3
−0.2
9.0 - 11.2 0.457 1.1+0.9−0.5 183 0.2+0.2
−0.1
11.2 - 13.4 0.442 4.1+3.6−2.0 190 0.8+0.7
−0.4
13.4 - 17.9 0.493 4.2+1.8−1.3 332 1.4+0.6
−0.4
17.9 - 22.4 0.466 4.3+1.7−1.2 328 1.4+0.5
−0.4
22.4 - 26.9 0.446 7.2+2.4−1.9 374 2.7+0.9
−0.7
Total 1815 7.0+1.4−1.0
energy bins are used to determine the energy-dependent discrimination power. The results
are shown in Table 3-1 and Figure 3-8. Additionally, the expected number of background
events in the WIMP acceptance window, Nleak, are shown, which are calculated based on
the predicted rejection and background rate in the 58.6 live-days exposure.
S1 [keVee] (2.2 p.e./keV)
1−R
ejec
tion 99.0%
99.9%
0 2 4 6 8 10 12 1410
−4
10−3
10−2
10−1
Figure 3-8. The ER rejection as a function of S1 for ∆log10(S2/S1) < µ. The rejectionimproves at lower energies, to better than 99.9% in the range 2–3 keVee.
The observed trend of the ER rejection power with energy is unexpected. If
recombination fluctuations were flat at all energies, or if the band widths were dominated
by binomial fluctuations from light collection, photoelectron emission, etc., one would
57
expect the band widths to grow at low energies, and hence the ER rejection power would
deteriorate. The opposite is observed, and is likely due to two factors. First, the ER and
NR bands themselves diverge slightly at lower energies. Second, the width of the ER band
does not grow at lower energies but instead remains relatively constant. Figure 3-9 shows
a decomposition of the ER band variance into statistical and anticorrelated recombination
fluctuations. It is quite evident that uncorrelated statistical fluctuations cannot alone
account for the observed degree of variance. Unfortunately, a model does not yet exist
that successfully predicts recombination fluctuations in liquid noble gases, and hence more
cannot be said on the subject besides emphasis on the need for its further study.
S1 [keVee] (2.2 p.e./keVee)
Ban
d V
aria
nce
[keV
ee2 ]
0 5 10 15 200
0.005
0.01
0.015
0.02
0.025
0.03Actual BandStatisticalAnticorrelated
Figure 3-9. Decomposition of the ER band variance. The anticorrelated recombinationfluctuations are inferred by comparing the expected statistical fluctuations tothe full observed band variance.
3.2 Electronic Recoil Band Shape
The background predictions, Nleak from Table 3-1, are sensitive to the predicted level
of electronic recoil rejection, Rer. The quantitative performance of this rejection, shown
in the same table, is in turn based upon the assumption that the ∆ log(S2/S1) spectrum
for electronic recoils is Gaussian distributed. This assumption seems reasonable, but
is difficult to justify given the relatively low statistics of the 137Cs calibration (Figure
3-6). What is known is that the width of the ∆ log(S2/S1) band is dominated by
58
fluctuations in the level of electron-ion recombination (Figure 3-9). If the distribution
of these recombination fluctuations are known, it is possible to simulate the shape of
the ∆ log(S2/S1) spectrum. The following section illustrates a measurement of this
distribution, which will then be used as the input to a Monte Carlo (MC) simulation to
determine the shape of the ∆ log(S2/S1) band.
3.2.1 Activated Xenon and the Combined Energy Scale
Following WS4, neutron-activated Xe, containing the isomeric sources 131mXe and
129mXe, was introduced to the XENON10 detector. The former has a half-life of t1/2 =
11.8 days and decays to the ground state in a single 163.9 keV transition usually in the
form of internal conversion electrons. The latter has a half-life of t1/2 = 8.9 days and
decays always in a series of two transitions, 196.6 keV followed by 39.6 keV, also usually
in the form of conversion electrons [57]. The lifetime of the 39.6 keV state, roughly 1 ns, is
too short to allow separate identification of the two transitions, and the observed signal
is instead that of a single 236.2 keV event. The preparation of this source is described in
detail in [58].
One advantage of these isomeric xenon calibration sources is that they diffuse
uniformly throughout the detector, and allow a characterization of the detector’s response
as a function of position. Additionally, the measurement with activated xenon allows a
calibration of XENON10’s combined energy scale (CES). This energy scale, described
later in Section 6.3, counts the total number of quanta, nγ+ne, and is insensitive to
recombination fluctuations.
These recombination fluctuations lead to an anticorrelation between the S1 and S2
signals, seen in Figure 3-10 (left). The calibration of S1 in number of total photons (nγ)
and S2 in number of electrons (ne) is done by adjusting the S1 and S2 scaling until the
major axis of the 131mXe ellipse has a slope of -1. This procedure leaves S1 and S2 in a
state such that their sum is proportional to the total quanta, and the absolute scaling is
then determined by nγ + ne = E/W , where E is the deposited energy (163.9 keV) and
59
S1 [nγ]
S2 [
n e]
129mXe
131mXe
0 2000 4000 6000 8000 10000 12000 140000
2000
4000
6000
8000
10000
12000
14000
0
50
100
150
200
250
300
350
400
450
Energy [keVee]
Cou
nts
0 50 100 150 200 250 3000
1000
2000
3000
4000
5000
6000
7000
8000CESS1S2
Figure 3-10. (Left) The activated xenon data, 131mXe and 129mXe with de-excitation linesat 164 keV and 236 keV, respectively, shown in S1 versus S2. The distinctanticorrelation is due to fluctuations in the fraction of recombiningelectron-ion pairs. The black dashed line indicates the major axis of the131mXe ellipse, and has a slope of -1. (Right) Spectra from the activatedxenon in S1, S2, and combined energy scale (CES); the improvement inenergy resolution of the combined scale is due its insensitivity torecombination fluctuations.
W = 13.5 eV [59] is the average energy required to produce a single quantum. The spectra
measured from the activated xenon in S1, S2, and CES are shown in Figure 3-10 (right).
The improvement in energy resolution gained by the CES is immediately apparent.
In order to determine the shape of the recombination fluctuations, events resulting
from 131mXe decays are examined. Data are selected based on Figure 3-10 (right), from
a narrow, ±12σ interval around about the 164 keV peak. Such a narrow range is chosen
so that nγ + ne is a constant value, and thus ne − nγ is a very accurate representation
of the recombination fluctuations, seen in Figure 3-11. The agreement between the
histogram and the Gauss fit even out to many σ is consistent with the hypothesis that the
recombination fluctuations are Gaussian-distributed. This assumption will be used as an
input to the MC described in the next section.
60
ne−nγ
Cou
nts
−6000 −4000 −2000 0 2000 4000 6000 8000
100
101
102
103
104
Figure 3-11. The spectrum of recombination fluctuations, in ne − nγ, along with a Gaussfit, from 164 keV decays of 131mXe. Data were selected from a narrow ±1
2σ
band about the mean of the peak in the CES spectrum.
3.2.2 Monte Carlo Construction
For all of the following, it is assumed that the recombination fluctuations are
Gaussian-distributed. The most natural starting point is to approximate the CES
spectrum of the low-energy 137Cs single scatter events, which is featureless and flat. A
set of random numbers from 1 to 40 is generated, and is assumed to represent the CES
energy spectrum in keV.
Because the CES is determined from counting quanta, the fraction of photons to total
quanta, nγ/(ne + nγ), versus CES gives a band whose width represents the recombination
fluctuations as a function of energy. Figure 3-12 (left) shows this band, along with
the band fit. The band fit is done by breaking up data into CES slices, and fitting the
nγ/(ne + nγ) spectrum of each slice with a Gaussian. Despite the relatively low statistics
from 137Cs data, the assumption that this band is Gaussian-distributed is justified due to
the observed Gaussianity of the 164 keV recombination fluctuations. Once the band fit
parameters are obtained from Figure 3-12 (left), a Gaussian-random number generator is
used to create a set of photon fraction values whose mean and standard deviation match
61
the red curves in Figure 3-12 (left), when applied to the previously-generated CES energy
values, described above.
CES [keVee]
n γ/(n e+
n γ)
0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Mean± σ
137Cs Data
1
1.5
2
2.5
3
3.5
4
S1 [keVee]
log 10
(S2/
S1)
MC (equal stats)
0 5 10 15 20 25 301
1.5
2
2.5
3
3.5
Figure 3-12. (Left) The photon fraction, which measures the electron-ion recombination,as a function of energy, from real 137Cs data. The mean (solid red line) andwidth (dashed red lines) are used as input to the MC. (Right) Thecomparison of the MC log10(S2/S1) versus S1 band to real data.
The photon fraction for each energy value then gives S1 and S2 in nγ and ne,
respectively, assuming perfect anticorrelation. These values are then both converted to
photoelectrons, with binomial fluctuations applied to simulate the realistic light collection,
quantum efficiency of the photocathodes, and collection efficiencies. The end result of this
process is shown in Figure 3-12 (right), where the log10(S2/S1) data and MC bands are
compared, based on equal statistics.
It is worth emphasizing that the goal of this MC is not so much to reproduce the
energy dependence of the band, but to accurately reproduce, and study, the shape of the
∆ log10(S2/S1) spectrum. The MC band from Figure 3-12 (right) is taken and “flattened”
by the same technique as the real data described in Section 3.1.3, to produce the quantity
of interest, ∆ log10(S2/S1). The 10 keVee≤S1≤ 12 keVee bin is chosen to compare MC
against data.1 Seen in Figure 3-13, the ∆ log10(S2/S1) spectrum is shown for the actual
1 The unit ‘keVee’ stands for ‘keV electron-equivalent’, defined in Section 2.4.3.
62
137Cs data, with the equivalent histogram generated by the MC, using equal statistics.
The degree of agreement between MC and data for this case suggests that the initial
assumption of Gaussian recombination fluctuations is valid.
∆ log10
(S2 / S1)
Cou
nts
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.80
10
20
30
40
50
60
70
80DATAMCMean from GaussFit±3σ from GaussFit
Figure 3-13. The equal-statistic spectrum of ∆ log10(S2/S1) for the 10-12 keVee bin, forboth real data and the MC. Also shown are the mean and ±3σ levels (greenlines).
3.2.3 Monte Carlo Results
Because the predicted leakage of the background data into the WIMP-search window
(Table 3-1) is based upon Gauss fits to the histograms of Figure 3-13, the goal of this
MC is to compare the predicted rejection based upon a Gauss fit (from here on referred
to as RG) to what the actual rejection is, as predicted by the MC (from here referred to
as RMC). The blue histogram in Figure 3-14 represents the same spectrum simulated in
Figure 3-13, but with 107 events. The magenta curve is a Gauss fit to the blue histogram,
and highlights its departure from Gaussianity.
Of interest is the departure of the blue histogram in Figure 3-14 from the magenta
curve, on the low end (because this is where the NR band appears). Interestingly, this
63
∆ log10
(S2 / S1)
Cou
nts
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.810
0
101
102
103
104
105
106
MCGaussFit± 3σ (from Fit)
Figure 3-14. The high-statistic MC spectrum of ∆ log10(S2/S1) for S1 in the range10-12 keVee. The departure of the blue histogram from Gaussianity,represented by the magenta curve, becomes readily apparent outside of ±3σ(red dashed lines).
is where there exists the largest degree of discrepancy. By studying the curves in Figure
3-14, a conversion is constructed between RG (magenta curve) and RMC (blue histogram).
Figure 3-15 shows the relation between RG and RMC , covering ten decades in RG.
For reference the region of interest in Figure 3-15 is the range 10−3 ≤ (1−RG) ≤ 10−2.
As mentioned before, the main purpose of this study is not to reproduce the energy
dependence of the ER band, but in modeling the shape of the ∆ log10(S2/S1). The
conversion curve of Figure 3-15 is applied to all energies in the WIMP search region of
interest (2-12 keVee).
Figure 3-16 (left) shows the previously-reported values of the rejection in blue, and
in red are the corrected values based on this MC. The uncertainties are based on the
original Gauss fits to the real data, and these remain the dominant uncertainty following
the corrections. These corrections scale directly to the total amount of predicted leakage
64
1 − RG
1 −
RM
C
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
10−7
10−6
10−5
10−4
10−3
10−2
10−1
100
MCEqual rejection
Figure 3-15. (1−RMC) versus (1−RG) for S1 in the range 10-12 keVee. At all values,(1−RMC) > (1−RG), with equal rejection indicated by the red line. Thetype of rejection characterizing the XENON10 WIMP search window is forrejection in the range 10−3 ≤ (1−RG) ≤ 10−2.
S1 [keVee] (2.2 p.e./keV)
1−R
ejec
tion
99.9%
99.0%
0 2 4 6 8 10 12 1410
−4
10−3
10−2
10−1
1− RG
with MC correction
Total: 11.5 +2.4 −1.6
S1 [keVee] (2.2 p.e./keV)
Nle
ak
0 2 4 6 8 10 12 140
1
2
3
4
5
6OriginalWith MC corrections
Figure 3-16. (Left) The original (blue) and MC-corrected (red) electronic recoil rejectionin the WIMP-search energy range. (Right) The corrected predictions on thenumber of background electronic recoils leaking into the WIMP searchwindow, from Table 3-1.
(Nleak), seen in Figure 3-16 (right). The previously-reported value of Nleak(original) =
7.0+2.1−1.0 shifts up to Nleak(corrected) = 11.5+2.4
−1.6.
65
3.2.4 Energy Dependence
The conversion of RG to RMC from Figure 3-15 has been taken to apply at all
energies within the WIMP search region. However, it is not guaranteed that this
assumption is valid. For example, because it has been assumed that the recombination
fluctuations are Gaussian-distributed, this also entails the implicit assumption that
the distribution is symmetric. The question then becomes, how do symmetric intervals
in photon-fraction space transform onto log10(S2/S1) space? In Figure 3-17, a set of
nγ/(ne+nγ)
log 10
(S2/
S1)
[p.e
./p.e
.]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5photon−frac. meanphoton−frac. − 10%photon−frac. + 10%
Figure 3-17. The mapping of a 0.2-wide symmetric interval from photon-fraction spaceonto log10(S2/S1) space. A clear asymmetry arises, whose polarity flips oneither side of the 50% photon fraction, or nγ/(ne + nγ) = 0.5.
symmetric intervals in photon-fraction space, with centers ranging from 0.1 to 0.9 with a
full width of 0.2 (i.e. ±0.1), is considered. The black curve is the mapping of the intervals’
centers onto log10(S2/S1) space, the blue and red curves are the mapping of the intervals’
lower and upper bounds, respectively. Clearly, symmetric intervals in photon-fraction do
not retain their symmetry when mapped onto log10(S2/S1). It is already clear from an
examination of Figure 3-14 that the ∆ log10(S2/S1) spectrum is asymmetric, but what is
now evident is that sign of the log10(S2/S1) skew might not always come out the same
way. Figure 3-17 shows that the skew of the log10(S2/S1) interval changes on either side
66
of nγ/(ne + nγ) = 0.5. This is important because, as Figure 3-12 (left) shows, the photon
fraction of the ER band crosses the 50% mark at roughly 6 keVee.
An additional complication is that the seven bins in S1 (from Table 3-1) have bounds
at constant S1, not at constant energy. The MC is constructed so that fluctuations in
photon fraction are Gaussian distributed at a given energy. But each S1 bin spans a range
of energy, while the curves in Figure 3-17 apply to only a single energy. Figure 3-18
CES [keVee]
n γ/(n e+
n γ)
S1 = 2 keVee
S1 = 12 keVee
3 keVee 4 keVee
5 keVee 6 keVee
8 keVee10 keVee
0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 3-18. The same data as in Figure 3-12 (left), with lines of constant S1 overlaid.Each curve corresponds to the bound of an interval of Table 3-1.
shows the photon fraction with the bounds of the seven WIMP search bins superimposed.
Clearly, the shape of the band in log10(S2/S1) space for bins of constant S1 depends quite
strongly on the way these bins intersect the band in Figure 3-18.
In order to address this issue, additional MC simulations are constructed to cover
the electronic recoil band over the full range of the WIMP search window. The results
are shown in Figure 3-19, for other WIMP search S1 energy bins. Not shown are the two
lowest bins, 2–3 keVee and 3–4 keVee as these exhibit the same qualitative behavior as the
spectra in the 4–5 keVee and 5–6 keVee bins.
67
4−5 keVee
100
101
102
103
104
105
106
5−6 keVee
Cou
nts
6−8 keVee
−1 −0.75 −0.5 −0.25 0 0.25 0.5 0.75
100
101
102
103
104
105
106
∆ log10
(S2/S1)
8−10 keVee
−0.75 −0.5 −0.25 0 0.25 0.5 0.75 1
Figure 3-19. The same ∆ log10(S2/S1) spectra as in Figure 3-14, but for various energyranges. Although the skew of the spectra does not remain the same, thenon-Gaussian tails on the low end are a consistent feature.
Though the spectra in Figure 3-19 do not maintain the same symmetry, all histograms
exhibit the same characteristic non-Gaussian tails at low values of log10(S2/S1). Each of
these simulations can again be used to formulate a conversion between the original
Gaussian-predicted rejection factors, RG, and those given by the MC. These updated
rejections are turned into MC-corrected background estimates, shown in Figure 3-20. The
new background estimate becomes Nleak(corrected) = 10.2+2.1−1.5.
3.2.5 Discussion
Based on an assumption of Gaussian-distributed recombination fluctuations, it is clear
that the electronic recoil band exhibits tails for low values of log10(S2/S1) in excess of the
Gaussian prediction. The spectrum of ne − nγ from the 131mXe calibration confirms this
assumption out to several standard deviations. Although it is not known whether this
behavior continues below 164 keV to the low energies relevant for the WIMP search, it is
68
S1 [keVee] (2.2 p.e./keV)
Nle
ak Total: 10.2 +2.1 −1.5
0 2 4 6 8 10 12 140
1
2
3
4
5
6OriginalMC corrections with E−dependence
Figure 3-20. Corrections to the values of Nleak reported in Table 3-1 based on theenergy-dependent MC results shown in Figure 3-19.
unlikely that any major changes occur because the photon fraction spectrum of Figure
3-12 (left) appears to be Gaussian distributed as well.
Though the results of the MC simulation indicate that the actual electronic recoil
rejection power is worse than the estimates given in Table 3-1, the consequences are
encouraging. What this means is that the background predictions based on the Gaussian
rejection, RG, actually underestimate the true background. Thus, any results that use
background subtraction based on Nleak are actually conservative results.
3.3 WIMP Search
The XENON10 experiment collected sourceless data in a series of five data runs,
designated WS1 to WS5 (WS stands for “WIMP Search”) occurring at various times from
April 2006 through September 2007. However, not all five data runs were used in the
actual blind analysis. WS1 and WS2 were used for detector characterization, and donned
the “WIMP Search” title because they involved only background events. WS5 occurred
after a modification of the triggering system, which unwittingly resulted in an increased
energy threshold, thereby providing no advantage in sensitivity over WS3 and WS4.
WS3 and WS4 represent a total of 58.6 live days of blind data, interrupted in
November for 137Cs source data used to define the low energy electron recoil band and
69
Figure 3-21. The live time of XENON10 during the duration of fall 2006 through winter2007. Blue and green points indicate calibration data that has been scaled toequivalent background live days based on the number of acquired triggers.Figure provided by L. deViveiros.
on December 1st for an AmBe calibration to define the nuclear recoil band (described in
Section 3.1.3). The progression of data collection throughout this time period is shown in
Figure 3-21. The details of the cuts and unblinding procedures can be found in [31, 60].
Following unblinding, the S1 and S2 values are used to construct the ∆log10(S2/S1) band
as in Section 3.1.3. Seen in Figure 3-22, this procedure results in ten events within the
WIMP search acceptance window. Though none of these events are likely to result from
nuclear recoils scatters, they are all considered in determining the experimental upper
limits described in the following sections. For a discussion of the likely origin of each of
these events, see [60].
3.3.1 Spin-Independent Interaction
Exclusion limits on the WIMP-nucleon cross section are calculated using the Yellin
Maximum Gap method [61]. This method is advantageous in that it allows a limit to be
set in the presence of both known and unknown backgrounds. The unknown background
is handled by comparing not only the measured number of events to the expected number,
but also comparing predicted and expected distributions. The “gap” between two events
70
S1 [keVee] (2.2 p.e./keV)
∆ lo
g 10(S
2/S
1)
NR Mean
NR −3σ
0 2 4 6 8 10 12 14 16 18−1.5
−1
−0.5
0
0.5
1
Figure 3-22. The distribution of blind WIMP search data in ∆log10(S2/S1) versus S1. Thesignal acceptance region is bounded horizontally by the blue lines andvertically by the brown lines. The ten events remaining in the acceptancewindow after cuts are indicated by the red circles.
adjacent in energy, x1,2, is defined by,
x1,2 ≡∣∣∣∣∫ Q2
Q1
dR
dQdQ
∣∣∣∣ , (3–1)
where Q1 is the energy of the first event and Q2 is the energy of the second. The
differential rate, dR/dQ, includes expected signal (Equation 2–2) and known background
(if any). A statistical parameter, C0, is calculated which represents the probability that
the maximum gap from a random sampling of dR/dQ would be smaller than the observed
maximum gap, and is given by,
C0(x, µ) = 1 +m∑
k=1
(kx− µ)k−1e−kx
k!(kx− µ− k). (3–2)
Here, x is the maximum gap, µ is the total number of expected events in the signal
acceptance window, and m is the largest integer ≤ µ/x. If no events are seen, then x = µ,
m = 1 and Equation 3–2 reduces to C0(µ, µ) = 1− e−µ, equivalent to the one-sided Poisson
null result.
71
The combined velocity of the Sun and Earth is taken as the time-averaged value. The
differential WIMP rate, Equation 2–2, is a function of cross section and WIMP mass. For
a given WIMP mass, the WIMP-nucleon cross section is varied until C0 = 0.9, representing
the 90% Confidence Level (C.L.) exclusion limit. The data shown in Figure 3-22 are
converted to nuclear recoil equivalent energy by assuming Leff = 0.19 at all energies.
WIMP Mass [GeV/c2]
WIM
P−
nucl
eon
cros
s−se
ctio
n [c
m2 ]
101
102
103
10−45
10−44
10−43
10−42
Figure 3-23. XENON10 58.6 live day SI WIMP-nucleon exclusion limits, in red. Thedashed line is with background subtraction, solid line is without. Resultsfrom a combination of CDMS-II 2008 data with a re-analysis of CDMS-II2004-2005 are shown in blue [37]. The shaded regions are favored by twostudies of MSSM models, dark [62] and light [63].
As discussed in Section 3.1.3, the expected number of background events can be
estimated under the assumption that the events in the ER band are Gaussian distributed
in ∆log10(S2/S1) space. These predicted backgrounds, per energy bin, are shown in
Table 3-1. The resulting 90% C.L. exclusion curves, with and without background
subtraction, are shown in Figure 3-23, along with the theoretically-favored regions of two
72
analyses of MSSM frameworks [62, 63]. Results from current best competing experiment,
CDMS-II [37], are also shown. A study of the actual deviation of the ER band from
Gaussianity is presented in Section 3.2. The uncertainty introduced by departures of
Leff from 0.19 is discussed in Chapter 4.
Figure 3-23 can be compared with Figure 1-8. XENON10, and more recently
CDMS-II, are now beginning to probe the interesting regions of the MSSM parameter
space relevant to the neutralino. The shaded regions of Figure 3-23 cover the 95% C.L.
region allowed by the analyses; the most favored regions are still outside the sensitivity
reach of existing searches.
3.3.2 Spin-Dependent Interactions
The general form of SD interactions was discussed in Section 2.2.2. In order to apply
these formulae to an actual detector, five pieces of information must be known. The first
two are the spin content of the nucleus, 〈Sp〉 and 〈Sn〉. The remaining three unknowns are
the spin structure functions, Sij (Equation 2–10). Whereas the SI interactions treat every
xenon nucleus in the fiducial region as a sensitive target, SD interactions couple only with
those nuclei having non-zero spin. The two naturally occurring xenon isotopes with spin
are 129Xe (J = 12) and 131Xe (J = 3
2), existing with natural abundances of 26.44% and
21.18%, respectively.
The nuclear structures of 129Xe and 131Xe cannot be considered identical, and
therefore must be treated separately. For 129Xe, there exist in the literature accurate
calculations based on two different effective nucleon-nucleon potentials, Bonn A [64] and
Nijmegen II [65]. The accuracy of the models is quantified by the agreement between
predicted and measured nuclear magnetic moment. This metric is chosen because
the matrix element for WIMP-nucleus scattering is very similar to that of the nuclear
magnetic moment.
These two models have also been applied to 131Xe, giving similar accuracies as in
the case of 129Xe. However, a third model exists for 131Xe based on the quasiparticle
73
Table 3-2. The spin expectation values for proton and neutron groups based on the threenuclear shell models discussed in the text. Also shown are the deviation of themodels’ predictions of the nuclear magnetic moment from the measured value,‘µ–acc.’. Values are taken from Table II of [67].
Nucleus Model 〈Sp〉 〈Sn〉 µ–acc.
129XeBonn A 0.028 0.359 19%Nijmegen II 0.0128 0.300 51%
131XeBonn A -0.009 -0.227 8%Nijmegen II -0.012 -0.217 50%QTDA -0.041 -0.236 1%
Tamm-Dancoff approximation (QTDA) [66]. This model yields a magnetic moment
accuracy to within 1% of the measured value, and is recommended for use over the
Bonn A and Nijmegen II models by the authors of [67]. The results of 〈Sp〉 and 〈Sp〉calculations based on the models described here are tabulated in Table 3-2, along with
their accuracies in terms of nuclear magnetic moment. In order to capture the level
of uncertainty introduced by the various nuclear shell models, limits are calculated
according to a ‘main’ model (Bonn A for 129Xe, QTDA for 131Xe) and an ‘alternate’ model
(Nijmegen II for 129Xe and QTDA for 131Xe). QTDA is used for 131Xe in both cases due to
its high degree of accuracy in the magnetic moment.
The spin structure functions are presented by Ressell and Dean [67] decomposed as an
exponential multiplied by a polynomial, given by,
Sij(y) = e−2y
(8∑
k=0
wij,kyk +
cij,9
1 + y
), (3–3)
where y ≡ (qb/2)2 is the unitless recoil energy, and b ' 1 fm A1/6 = 5.068×10−3 MeV−1 A1/6
is a measure of the nuclear size. The coefficients wij,k are tabulated in [67] for Bonn A and
Nijmegen II. A parameterization of the 131Xe spin structure functions based on the QTDA
model is not found in [67] or even in the original paper [66]. Bednyakov and Simkovic [68]
have attempted to extract a set of Sij values from Figure 3 of [66], however, these values
provide only coarse coverage in the region of interest for XENON10’s dark matter search.
74
Table 3-3. The polynomial coefficients of a fit to the QTDA spin structure functionsshown in Figure 3 of [66]. The functions are parameterized as a function of q2
as Sij =∑5
k=0 ckq2, with q in units of GeV c−1.
mode c5 (×107) c4 (×106) c3 (×104) c2 (×103) c1 c0
S00 -5.4628 3.4638 -8.9189 1.1992 -8.7745 0.0375S11 -2.3048 1.6063 -4.4275 0.6139 -4.4670 0.0175S01 3.5405 -2.7828 8.7248 -1.3769 11.2749 -0.0498
The QTDA spin structure functions are here determined in a way that is more
appropriate for XENON10. The Sij curves in Figure 3 of [66] are copied into the
GraphClick software [69], where a set of points is extracted from each curve. These
points are then fit with a fifth-order polynomial in the low energy region, shown in Figure
3-24, with polynomial coefficients tabulated in Table 3-3. The fits are valid for values of
q2 . 0.015GeV2 c−2.
q2 [GeV2 c−2]
Sij(
q)
0 0.005 0.01 0.015 0.02−0.05
−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
QTDA S00
QTDA S11
QTDA S01
polyfitsXENON10 energy range
Figure 3-24. The QTDA spin structure functions for 131Xe. Open circles are taken fromFigure 3 of [66], solid lines are the polynomial fits shown in Table 3-3. Theenergy range used for the WIMP search of XENON10 is indicated by theshaded yellow region.
The exclusion limits for SD coupling have been normalized to pure proton and pure
neutron couplings as defined in Equation 2–9. Results are shown in Figure 3-25 for the
75
‘main’ and ‘alternate’ nuclear shell models. Exclusion limits are again calculated based on
the Maximum Gap parameter C0 (Equation 3–2). As both of the xenon isotopes discussed
here have an unpaired neutron, most of the nuclear spin is carried by the neutron group
(Table 3-2). As a result, the XENON10 exclusion limit on pure neutron coupling is
significantly more constraining than that for pure proton coupling.
WIMP Mass [GeV/c2]
SD
pur
e pr
oton
cro
ss s
ectio
n [c
m2 ]
101
102
103
10−39
10−38
10−37
10−36
10−35
10−34
WIMP Mass [GeV/c2]
SD
pur
e ne
utro
n cr
oss
sect
ion
[cm
2 ]
101
102
103
10−40
10−39
10−38
10−37
10−36
Figure 3-25. The XENON10 SD exclusion limits normalized to pure proton (left) andpure neutron (right) for main (solid red) and alternate (dashed red) spin formfactors. The results the best competing direct detection experiments in eachcategory are shown for comparison: COUPP–dark blue [40]; KIMS–black [39],CDMS-II–light blue [37]. The shaded area is the theoretical 95% probabilityregion from one analysis of CMSSM [63].
The decision to hold the 131Xe model fixed for both main and alternate shell models is
justified because the variation in the exclusion limit is dominated by the 129Xe model. The
WIMP-neutron exclusion limit is shown in Figure 3-26 (left) for four sets of shell model
choices. It is clear that the chosen 131Xe shell model has only a very small effect on the
resulting exclusion limit.
An alternative way of interpreting the XENON10 results is to constrain the SD
WIMP-nucleon couplings themselves, ap and an. From Equation 2–8, it is clear that
dR/dQ ∝ [ap〈Sp〉+ an〈Sn〉]2. Therefore, for a given nucleus, any pair of values of ap and an
that lie along the line,
ap = −an〈Sn〉〈Sp〉 , (3–4)
76
result in a null cross section and no events. However, with the existence of two SD-sensitive
isotopes, a closed exclusion contour can be formed in ap-an parameter space. Seen in
Figure 3-26 (right) for a WIMP mass of 50GeV c−2, a value of C0 (Equation 3–2) is
assigned to each point in the parameter space. The 90% C.L. exclusion is then given by
the contour defined by C0 = 0.9. Also shown are the 129Xe and 131Xe axes of null cross
section (Equation 3–4).
WIMP Mass [GeV c−2]
SD
pur
e ne
utro
n cr
oss
sect
ion
[cm
2 ]
20 30 40 50 60 70 80 90 100
10−38
BonnA for 129Xe, QTDA for 131Xe
Nijmegen II for 129Xe, QTDA for 131XeNijmegen II for Both isotopesBonnA for Both isotopes
an
ap
−0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8−8
−6
−4
−2
0
2
4
6
8
C0 = 0.9 Contour
C0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
129Xe
131Xe
Figure 3-26. (Left) The WIMP-neutron exclusion limit calculated for four differentcombinations of 129Xe and 131Xe shell models. It is clear that the shell modelsfor 129Xe produce the greatest variation in the resulting exclusion limit.(Right) The C0 map for 50 GeV c−2 WIMPs, along with the correspondingcontour that excludes the exterior parameter space at the 90% confidencelevel. The dashed lines indicate the 129Xe and 131Xe axes of null cross section.
3.3.3 Prospects for the Heavy Majorana Neutrino
Section 1.3.1 covered the topic of the cosmological abundance of relic neutrinos. If
one ignores arguments related to the formation of large scale structure, Equations 1–11
and 1–12 alone require that the heaviest neutrino species must have a mass less than
∼10 eV cm−2 so that their density does not conflict with measurements of Ωm. It is already
known that none of the Standard Model neutrinos even come close to exceeding this mass,
but it could be possible that more neutrinos exist, possibly part of a fourth generation
of fermions. Equation 1–12 applies only to neutrinos that freeze-out relativistically, but
77
“heavy” neutrinos, with mass greater than ∼2GeV, would freeze-out cold with a relic
density less than Ωm [70].
The relic density of a heavy neutrino would be too small to account for the dark
matter under the standard freeze-out scenario [71]. However, given a dynamically evolving
dark energy density prior to BBN, it could be possible for heavy neutrinos to be produced
with an abundance large enough to account for Ωm [72]. A heavy Dirac neutrino would
interact with normal matter via SI interactions, but has long since been ruled out as a
possible dark matter candidate by previous direct detection experiments [73].
In contrast, a heavy Majorana neutrino interacts only via SD interactions, and its
elastic scatter cross section with nuclei is given by [74, 75],2
σνN =8
π4G2
F m2r[ap〈Sp〉+ an〈Sn〉]2
(J + 1
J
), (3–5)
which is identical to Equation 2–8 except for the prefactor. Such a heavy Majorana
neutrino with mass in the range ∼100–500GeV c−2 has been predicted in minimal [72]
and walking [76] technicolor theories. These models provide a mechanism for electroweak
symmetry breaking that is alternative to the Higgs mechanism, and posit the existence of
new gauge interactions with non Standard-Model fermions.
Unlike the SD WIMP-nucleus cross section, here ap and an are given from particle
physics experiments. The couplings are taken to be ap = 0.68 and an = −0.58 [36, 77,
78].3 With these values, and the nuclear properties given by the main and alternate shell
models presented in Section 3.3.2, the cross section in Equation 3–5 depends only on
the neutrino-nucleus reduced mass, mr. This cross section is then used to find C0 as a
2 The cross section in Equation 6.2 of [36] differs by a factor of four, but this appears tobe a mistake.
3 Values in [36], based on [77], are given only as a2p,n and hence do not preserve the sign
of the coupling. The authors provide [78] as a web supplement with the full values.
78
function of the neutrino mass, Mν,Maj, and is shown in Figure 3-27. The C0 versus mass
νMaj
Mass [GeV/c2]
C.L
. Exc
lusi
on b
y X
EN
ON
10
Excluded
by LEP
101
102
103
104
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Main Form FactorsAlternate Form FactorsExcluded by XENON10 at 90% C.L.
Figure 3-27. The confidence level of exclusion of the heavy Majorana neutrino, given bythe Maximum Gap parameter, C0. The Majorana neutrino is thereforeexcluded at the 90% C.L. where the curve is greater than C0 = 0.9, indicatedby that horizontal black dotted line. Majorana neutrinos with mass less thanhalf the Z boson have been excluded by the Large Electron-Positroncollider [79], indicated by the vertical dashed line.
curve crosses C0 = 0.9 at 9.4GeV c−2 and 2.2TeV c−2 using the main shell model, and
9.6GeV c−2 and 1.8 TeV c−2 using the alternate shell model. Heavy fourth-generation
neutrinos with a mass less than half the Z boson mass (45.6GeV c−2) have already been
excluded at the Large Electron-Positron collider (LEP) [79], indicated by the vertical
dashed line in Figure 3-27. Although Majorana neutrinos with Mν,Maj > 2.2TeV are
not excluded by cosmological constraints [71], technicolor heavy neutrinos are unlikely to
have a mass greater than ∼500GeV c−2 [72], and therefore the lower limit on Mν,Maj given
by XENON10 and LEP effectively rules out these particles as a significant contributor
to Ωm. It is worth emphasizing that the constraints shown here apply only to the heavy
Majorana neutrino as a dark matter candidate. If none of the special pre-BBN dynamical
79
dark energy conditions existed to allow ΩνM≈ Ωm, then such a fourth-generation neutrino
could still exist, albeit with no cosmologically-interesting abundance.
80
CHAPTER 4MEASUREMENT OF Leff WITH THE XECUBE DETECTOR
There are two kinds of people, those who do the work and those who takethe credit. Try to be in the first group; there is less competition there.
-Indira Gandhi
4.1 Leff and the Need for its Further Study
The relative scintillation efficiency of liquid xenon to nuclear recoils, Leff , was
discussed in Chapter 2. Because the WIMP recoil spectrum in LXe is expected to be
steeply falling with energy, as compared with lighter target nuclei (see Chapter 2), the
understanding of the nuclear recoil energy scale strongly affects the conclusions drawn
from dark matter searches that use LXe.
Nuclear Recoil Energy [keV]
Lef
f
XENON10Zeplin−II
101
102
0
0.1
0.2
0.3
0.4
0.5
Figure 4-1. A survey of Leff measurements in the literature prior to 2009. Blue trianglesare from [49], green squares from [48], with the remaining measurements citedlater in this chapter. The purple and red vertical lines correspond to theenergy ranges used by Zeplin-II [80] and XENON10 [31], respectively. Thebeige shaded area is used as an estimate of the uncertainty of Leff inXENON10’s results.
Figure 4-1 shows the measurements of Leff in the literature prior to 2009. The
Zeplin-II dark matter search [80] operated in an energy regime that has been well-studied,
81
while the XENON10 measurement suffers from quite sparse coverage. The two measurements
in XENON10’s energy range by Aprile [49] and Chepel [48] appear to indicate opposing
trends with decreasing energy. While the choice in XENON10 to use a flat Leff =0.19 is
fairly well justified, given the existing high-energy measurements, there is clearly a large
uncertainty introduced, indicated by the beige shaded area in Figure 4-1. The uncertainty
in the low-energy behavior of Leff can be propagated through to the final results of
XENON10, indicated by the beige region in Figure 4-2, and represents XENON10’s
largest systematic uncertainty. It becomes clear that an improved understanding of Leff ’s
low-energy behavior is necessary, requiring new measurements.
WIMP Mass [GeV/c2]
WIM
P−
nucl
eon
Cro
ss S
ectio
n [c
m2 ]
101
102
103
10−44
10−43
10−42
Figure 4-2. The XENON10 upper limit on the spin-independent WIMP-nucleon crosssection. The beige area indicates the limit’s uncertainty corresponding to thebeige region in Figure 4-1
4.2 Methods for Measuring Leff
4.2.1 Measurement Technique and Facility
Determination of Leff requires the production of nuclear recoils whose energies are
known independent of their response in the LXe. The technique is similar to that used
in Compton scatter measurements, but using neutrons instead of gamma rays. Nearly
82
θ
LXe
EJ301
np
Paraffin
Pb
T(p,n)3He60 cm
50 cm
Figure 4-3. Schematic diagram of the experimental setup. Incoming 1 MeV neutronsscatter in the LXe and are tagged by the EJ301 organic scintillator at anglesof 48, 62, 70.5, and 109.5. The paraffin and lead are used to shield theEJ301 from direct neutrons and gamma rays.
monoenergetic neutrons are incident upon a LXe target, some of which scatter under
an angle θ and are collected with an EJ301 organic scintillator (see Fig. 4-3), capable of
distinguishing electronic (gamma rays) from nuclear (neutron) recoils via Pulse Shape
Discrimination (PSD) [81, 82]. EJ301 is a proprietary name; the scintillator material is
also known by the proprietary names BC501A and NE213. In this way, the energy of the
recoiling xenon nucleus is known kinematically, and is given by the relation
Er =2En
(1 + A)2[1 + A− cos2 θ − cos θ
√A2 + cos2 θ − 1] ≈ 2EnA
(1 + A)2(1− cos θ), (4–1)
where Er is the recoil energy, En is the energy of the incoming neutron, A is the
mass number of the target nucleus, and θ is the scattering angle in the lab frame (the
approximation is valid when A À 1 and En ¿ mnc2, mn being the mass of the neutron).
The measurements were conducted in the neutron beam of the Radiological Research
Accelerator Facility (RaRAF) at the Columbia Nevis Laboratory, also described in
a previous study of Leff [49]. In the present work, 1.9MeV protons are incident on a
tritium target, yielding 1MeV neutrons in the T(p,n)3He reaction. This reaction produces
83
neutrons over all 4π s.r., however, the luminosity is peaked in the forward direction and
the energy variation due to the angular spread of the 1” LXe cell, 60 cm distant from the
tritium target, is less than 0.09% [83]. The terminal voltage of the proton accelerator (and
hence the incident proton energy, Ep) is known to within 0.1%. These two systematic
uncertainties, coming from the angular dependence of En and the uncertainty in Ep,
are considered negligible and are not included in the calculations of section 4.3.2. The
dominant spread in the incident neutron energy comes from the thickness of the TiT2
target, in which the protons can lose up to 260 keV before producing neutrons [84]; this
translates to a 1-σ spread of ±7.8% in En.
Also seen in Figure 4-3, a 30 cm-thick paraffin block is placed along the line of sight
between the tritium target and the EJ301 scintillator, in order to block neutrons from
directly interacting in the EJ301. In addition to the paraffin block, 5 cm of Pb shield the
EJ301 from gammas produced in the T(p,n)3He reaction.
4.2.2 The Xecube Detector
The LXe detector allows a zero-field measurement of the scintillation signal with
>95% of the interior surface viewed by photon detectors. A schematic of the detector
design is seen in Fig. 4-4. The LXe volume is viewed by six 1 in2 Hamamatsu metal
channel R8520-06-Al photomultiplier tubes (PMTs), four of which use a new bialkali
photocathode that yields quantum efficiencies to 178 nm light around 40% at room
temperature [85]. The PMTs, held together with a polytetrafluoroethylene (PTFE)
frame, form a cube such that each PMT window covers a face of the cube. Both the
photocathode and metal body of the PMTs are held at ground potential, with positive
high voltage applied to the anodes. This configuration guarantees that no residual electric
fields existed in the LXe, whose scintillation yield can be strongly dependent on the
applied field [56] (by definition, Leff is the relative light yield at zero field).
The xenon is cooled and liquefied by a copper ring cold finger which is thermally
coupled to a liquid nitrogen bath, and the xenon liquid level kept above the top PMT.
84
1"PMTPMT
PMT
PMT
PTFE
LXe
GXe
To
LN2
Coldfinger
Pumping, Filling, Cables
Liquid level
Fiberglass Insulation
Figure 4-4. Schematic diagram of the LXe chamber used for the Leff measurement.Visible are four of the six PMTs used to view the 1 in3 LXe volume. Cooling isachieved by the copper cold finger above; temperature and pressure areregulated by heaters (not shown) placed on the stainless steel vessel.
The temperature is held constant at 180K (same as in XENON10 [31]), with fluctuations
varying by less than 0.03%. The entire detector assembly is contained in a stainless steel
vacuum vessel, surrounded by fiberglass for thermal insulation from the outside world.
Following assembly and xenon liquefaction, the detector is moved into the beam room.
The EJ301 scintillator is contained in an aluminum cylinder 3” in diameter and 3”
tall, held at room temperature. The liquid is viewed by a single Photonis XP4312B PMT
and read out with the same electronics as the PMTs in the LXe chamber.
85
Monte Carlo particle transport simulations are conducted in order to assess the
systematic uncertainties and backgrounds. Included in these simulations are the full
geometry of the experimental setup, angular spread of the neutron beam, and the energy
spread of the incident neutron energies. The simulations use the Geant4 simulation
toolkit, version 4.8.3 [86], with neutron scattering cross sections taken from the JEFF-3.1
databases. The results of the simulations are discussed further in section 4.3.2.
4.2.3 Data Acquisition
Start
Stop
EJ301
Amplifiers Trigger
TAC
ADC
TriggerSignal
LXe
Figure 4-5. Schematic diagram of the data acquisition system used with the Xecubedetector. The six channels from the LXe are added in to three channels of twofor the triggering system, requiring coincidence between these three channelsand the neutron scintillator (EJ301).
A schematic diagram of the triggering and data acquisition system is seen in Fig. 4-5.
The analog PMT signals are fed into a Phillips 776 amplifier with a gain of 10, with
two identical outputs per channel. One output is digitized by a CAEN 8-channel V1724
100MHz flash ADC, while the other output is fed to the triggering system.
For the LXe trigger, the six LXe PMT channels are combined in pairs with FAN
modules, to produce three triggering channels, connected to discriminators set to trigger
at the single photoelectron (p.e.) level. The logical outputs of the three discriminator
86
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.2
0.4
0.6
0.8
1
Energy [keVee]
Tri
gger
Eff
icie
ncy
Figure 4-6. The efficiency of the LXe trigger condition, based on a Monte Carlosimulation. The trigger requires that all three pairs of trigger channels receiveat least one photoelectron each. Though the PMTs signals are combined intopairs for the trigger, the channels are digitized individually.
channels are passed to an N = 3 coincidence unit. Thus, the LXe trigger condition is
similar to a simple N ≥ 3 p.e. requirement, but with the added stipulation that the N
p.e. must be distributed to certain PMTs (i.e. if a single p.e. is received in PMTs 1, 4, and
6, this can produce a trigger; a single p.e. received in PMTs 1, 2, and 6 cannot because 1
and 2 are combined in the same trigger channel). The efficiency of this trigger condition is
determined by the Monte Carlo method. Seen in Fig. 4-6, it indicates ∼100% efficiency at
1 keVee, slowly rolling off to ∼90% at 0.5 keVee. The EJ301 trigger is taken simply as the
output of the discriminator.
For the measurement of the neutrons’ Time of Flight (ToF) the LXe trigger is fed
directly to the “start” input of a Time-to-Amplitude Converter (TAC), Ortec 556, while
the EJ301 trigger provides the “stop” after appropriate delay. The output of the TAC is
digitized by the same CAEN unit. Calibration of the ToF signal is discussed further in
section 4.3.1.
The shape of the signal in the EJ301 depends on the incoming particle species, and
can be used to distinguish neutrons from gamma rays since the characteristic scintillation
decay time is different for these particles. This can be explained by the presence of
87
bimolecular interactions that convert long-lived triplet excited states into short-lived
singlet excited states, resulting in a delayed fluorescence emission. The rate of these
bimolecular interactions depends on the density of triplet states, which in turn depends on
the rate of energy loss dE/dx of the recoiling particle. Thus, the tails of pulses resulting
from nuclear recoils (high dE/dx) will be characteristically longer than those from
electronic recoils (low dE/dx) [81]. In EJ301, the “slow” component is two orders of
magnitude longer than the “fast” component, reported to be 3.2 ns [87]. A PSD parameter
is constructed by dividing the area of the pulse’s tail by the total area of the pulse, with
the tail defined as the part of the trace starting 30 ns after the peak until the trace reaches
5% of the peak value.
4.3 Analysis and Results
4.3.1 Calibrations
The PMTs are calibrated in situ with a pulsed blue LED, in order to measure the
gain. The light from the LED produces a single p.e. spectrum, whose mean determines the
gain of the multiplier chain. With a complete set of such LED calibration measurements,
the signals obtained for all acquisitions can be converted to a value in number of p.e.
The relationship between the number of collected p.e. and the total number of emitted
photons depends on the geometrical light collection efficiency, the quantum efficiency of
the photocathodes, and the collection efficiency between the photocathode and the first
dynode. Although these values are not known to high precision, they represent completely
linear processes and hence lead to a linear relationship between the total number of
scintillation photons and the measured number of p.e. Comparing the p.e. yields of various
sources thus gives a measure of their relative scintillation yields.
As Leff is defined against the scintillation yield of 122 keV gamma rays, data from
a 100µCi 57Co source are taken periodically during the experiment. Fig. 4-7 shows the
spectrum from one such calibration. The 57Co yield is measured to be 19.64 ± 0.07
(stat) ± 0.11 (sys) p.e./keVee, where the statistical uncertainty is the combination of the
88
Number of Photoelectrons
Cou
nts
0 1000 2000 3000 4000 50000
200
400
600
800
Figure 4-7. The scintillation light spectrum of 122 keV gamma rays from 57Co, used tocalibrate the electronic recoil energy scale. This calibration gives a scintillationyield of 19.64 p.e./keV.
parameter uncertainties of the fits from the various calibration data, and the systematic
uncertainty is taken from the variation in this yield over the two-day duration of the
experiment. One set of PMT gain values is applied to all data, and thus the systematic
uncertainty in the 57Co yield quoted above accounts for both variations in yield and PMT
gain.
In addition to 57Co, data were also collected from a 22Na source. This source emits a
β+ that promptly loses energy in the Na and annihilates, producing two 511 keV gamma
rays emitted simultaneously in opposite directions. With the source placed between the
LXe detector and the EJ301 detector, the two gamma rays will interact at essentially
the same time in the two detectors. In this way, 22Na provides a baseline ToF=0 which,
when used in conjunction with a variable delay generator, is used to calibrate the ToF
measurement system.
4.3.2 Event Selection, Backgrounds, and Results
The processing of the data acquired at each angle yields two parameters which can be
used to select events of interest: the event ToF, and the PSD parameter from the neutron
89
detector. Fig. 4-8 shows the distribution of events in PSD parameter and ToF. Clearly
visible are the nuclear recoil and electronic recoil bands, in addition to the peaks from
both gamma and neutron scatters. The PSD cut is chosen to accept a majority of the
nuclear recoil band while rejecting electronic recoils. The width of the ToF cut is 10 ns,
which is the expectation based on the spread in En and the finite size of the detectors.
The tail of the ToF peak is due mainly to events where the neutron scattered in one of
the detector materials in addition to the LXe, before interacting in the EJ301 scintillator.
Multiple scatters in the LXe also add to the tail, although M.C. simulations indicate that
their overall contribution is less than 2%.
Time of Flight [ns]
PSD
, tai
l/tot
al
Accidentals Neutrons
0 10 20 30 40 50 60 70 80
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Figure 4-8. The distribution of triggered events in PSD vs. ToF space from the data set at70.5. An “upper” band and “lower” band are readily identifiable in the data,and correspond to nuclear recoils and electronic recoils, respectively. The peakat the lower left near ToF=0, due to gamma rays that Compton scatter in theLXe before striking the EJ301, is easily vetoed by the PSD cut. A populationof accidental triggers (see text) having a flat ToF spectrum is visible in bothbands and contributes background events within the neutron peak. The LXespectra of events within the left box are used as the expectation of thisbackground. The width of the right box—10ns—is chosen to accept neutronsthat interact in any region of the finitely-sized detectors.
90
Energy [keVee]
Cou
nts
(a)
0 1 2 3 4 50
20
40
60
80
100
Energy [keVr]
Cou
nts
(b)
0 10 20 30 400
50
100
150
200
Figure 4-9. Selected results of the Monte Carlo simulations, which do not include theaccidentals background. (a)–The spectrum of events tagged at 70.5, scaledwith the measured value of Leff giving the electron-equivalent energy (keVee),convoluted assuming Poisson statistics for the number of p.e. and multipliedby the simulated trigger efficiency curve. The green histogram is the totalspectrum, and the black circles indicate the true materials background. Thered dashed line is an exponential fit to the high-energy region of the greenhistogram; its agreement with the true materials background confirms thevalidity of this technique’s use in the real data. The shaded blue area showsthe spectrum of true elastic single scattered neutrons. (b)–The spectrum ofevents tagged at 109.5. The data are shown in the original, recoil equivalentenergy scale (keVr) without Poisson convolution. The materials background inthis region departs from the exponential behavior seen at lower energies, anddistorts the position of the peak from true single scatters, at 20 keV. The reddashed lines are the result of an exponential+Gaussian fit. The Gaussiancomponent, centered at 22.94± 4.34 keV, is used as the ‘true’ energy of theGaussian component in the real spectrum.
Two backgrounds contribute to the LXe spectrum which cannot be vetoed with
the cuts described above, and must instead be subtracted. It is clear from Fig. 4-8 that
beneath the neutron peak lies a population of events which have a flat ToF spectrum.
These are identified as neutrons that accidentally interact in the EJ301 in coincidence
with an unrelated event in the LXe, and are referred to as accidentals. As these events are
uniform in ToF space, accidentals outside of the ToF peak should have the same energy
spectrum as those within the peak. The LXe spectrum of the events inside the box of
91
Fig. 4-8 labeled “accidentals” is used as the expectation of the accidentals background.
The region to the left of the peak is chosen because the peak’s extended tail contaminates
the accidentals spectrum to the right of the “neutron” peak.
The second background that cannot be vetoed comes from neutrons that scatter
in various detector materials in addition to the LXe, before interacting in the EJ301.
Here referred to as materials background, MC simulations show that the spectrum of
these events in the LXe follows an approximately exponential distribution in the region
of the peak. Fig. 4-9(a) displays the results of the MC simulation of the data set at
70.5, indicating the contribution from the materials background. In order to estimate
the spectrum of these events in the real data, a decaying exponential was fit to the high
energy portion of the distributions after subtracting the accidentals background.
After applying cuts (PSD and ToF) and subtracting backgrounds (accidentals and
materials), a spectrum results in which the peak from single-scatter neutrons can be
readily identified, seen as the solid circles in Fig. 4-10. The horizontal scale of these
spectra is given as “keVee” meaning “keV electron-equivalent”, indicating it is the energy
scale derived from the 57Co calibration. Leff is found from the following relation:
Leff =Eee
Enr
, (4–2)
where Eee is the electron-equivalent energy (based on the 122 keV scintillation yield) and
Enr is the true recoil energy. Thus, when these spectra are fit with Gaussian functions,
the estimators of the mean, divided by the true recoil energy, give the Leff values at these
energies.
The uncertainties in the recoil energies are taken directly from the spread in the
incident neutron energy combined with the geometrical uncertainty due to the finite size
of the detectors. These values are obtained from the MC simulations and are listed in
the second column of Table 4-1. The uncertainties in Leff are calculated by considering
the spread in Er mentioned above, statistical errors in the Gaussian fits, the variation
92
Energy [keVee]
Cou
nts
48°
(a)
0 0.5 1 1.5 2 2.5 3
0
50
100
150
200
Energy [keVee]
Cou
nts
62°
(b)
0 1 2 3 4 5
0
20
40
60
80
100
120
140
Energy [keVee]
Cou
nts
70.5°
(c)
0 1 2 3 4 50
20
40
60
80
100
120
140
Energy [keVee]
Cou
nts
109.5°
(d)
0 2 4 6 8 100
50
100
150
200
250
300
350
Figure 4-10. The spectra of events in the LXe for the four angles used in this study:(a)-48; (b)-62; (c)-70.5; (d)-109.5. In all four plots, the black dot-dashedline is the original spectrum, black dashed line is the spectrum of accidentals(see Fig. 4-8), green line is the spectrum after subtracting the accidentalsbackground, shaded-gray region is the exponential fit to the tail of the greenspectrum and used as the expectation of the materials background, and theblue dots are the spectra after subtracting both backgrounds. Error bars onthe blue dots are the combined errors of the original, accidentals, andmaterials background (the gray area covers the 1-σ region of the fitparameters), and are included in the Gaussian fit to the blue dots, indicatedby the solid blue curves.
in 57Co light yield, the uncertainty in the background estimations, and the effect of
the trigger threshold roll-off. This last uncertainty was calculated by finding the peak
positions before and after dividing the spectra by the trigger efficiency discussed in
section 4.2.3. However, only the lowest angle (48) is affected by this trigger roll-off. The
asymmetric error bar of the 5 keV data point is due to both the trigger roll off and the
93
actual parameter uncertainty in the Gaussian fit. For all angles, the dominant contribution
to the uncertainty in Leff is from the spread in Er.
Table 4-1. The values of Leff obtained at the four angles used in this study. Error bars onthe recoil energies are the spread of En as mentioned in section 4.2.1 combinedwith the geometrical uncertainties. The uncertainties in Leff are thecombination of all statistical and systematic errors mentioned in the text.
θ Er (keV) Leff
48 5± 0.68 0.141+0.025−0.037
62 8± 0.91 0.137± 0.01670.5 10± 1.06 0.140± 0.016
109.5 22.94± 4.34 0.205± 0.039
Though the purpose of this study is to investigate the behavior of Leff below 10 keV,
it is necessary to collect data from higher-energy recoils in order to establish a connection
with previous studies. For this, the EJ301 is placed at a scattering angle of 109.5,
corresponding to 20.0 keV recoils. However, this angle is close to the minimum in the
differential scattering cross section of 1MeV neutrons in Xe [88], and so the signal
from “true” single scatters is well below the background. Additionally, the materials
background in this energy range departs from a decaying exponential. As can be seen in
the MC data of Fig. 4-9(b), the actual “bump” in the spectrum, coming primarily from
neutrons which have also scattered in the PTFE, is actually slightly higher than 20 keV. In
order to find the true energy of the peak position, the same procedure used in examining
the real data was applied here to the MC data, giving a recoil energy of 22.94 ± 4.34 keV.
The spread in Er is taken as the width of the Gaussian component in the MC spectrum.
The values obtained for Leff [47] are listed in Table 4-1, and additionally shown
in Fig. 4-11 along with the results of previous studies [48–52]. Shown as well is the 1-σ
allowed region of the best-fit procedure described in section 4.4.
4.4 Indirect Method
Use of a coincidence tagging experiment with a monoenergetic neutron beam is the
most direct method of determining Leff . However, it is not the only available technique.
In addition to coincident beam data, Xecube collected data from a 2Ci AmBe source that
94
Nuclear Recoil Energy [keV]
Leff
101
102
0
0.1
0.2
0.3
0.4
0.5
Figure 4-11. Measured Leff values as a function of Xe nuclear recoil energy. Symbolscorrespond to ()–this work [47]; (¤)–Chepel et al. [48]; (4)–Aprile etal. [49]; (♦)–Akimov et al. [50]; (×)–Bernabei et al. [51]; (5)–Arneodo etal. [52]. The solid gray curve is the result from a best-fit analysis ofXENON10 AmBe source data and MC [53]. Also shown is the theoreticalprediction of Hitachi (dashed line) [45]. The shaded-blue region is the resultof the Xecube best fit between AmBe source and Monte Carlo.
emits neutrons via the (α,n) reaction. The AmBe branching ratio for neutron emission is
6× 10−5 [89], giving ∼ 4× 106 neutrons/s.
The Geant4 Monte Carlo (M.C.) package provides only energy deposition and particle
tracking information, and does not simulate scintillation mechanisms in detector materials.
Hence, one extracts the absolute energies from particle hits, regardless of the interaction
type (i.e. electronic versus nuclear recoils). Therefore, in order to compare a spectrum
from an AmBe simulation to that from real data, the simulated hit energies must be
scaled first by Leff . If, however, Leff is considered a parameter, it is possible to estimate
95
Leff by comparing the simulated and real spectra. Leff is varied until the agreement of the
two spectra is optimized.
In order to perform such a study, a functional form of Leff must first be chosen, and
its functional parameters varied according to the best-fit procedure. Herein lies a problem,
because the functional form chosen should not artificially bias the Leff estimation to
take on a particular shape characteristic of the chosen function. Perhaps the best way
to overcome this hurdle is to model Leff with a cubic spline, interpolated between knots
at fixed nuclear recoil energies, and treat the value of the knots as free parameters. This
way, Leff is smooth with continuous first and second derivatives, and its energy-dependent
behavior is not fixed to follow a particular trend. P. Sorensen performed an analysis in this
manner, comparing the M.C. and real AmBe spectra taken in XENON10 [53], the results
of which are included in Figure 4-11.
A rigorous measurement of Leff with this technique (as done by Sorensen) is
difficult and extremely time consuming, for two reasons. First, one should work with
a sufficient number of spline knots, covering the entire energy range of the spectrum, so
as to capture all of Leff ’s energy-dependent features. However, the task of extracting
a best-fit increases in complexity dramatically as the number free parameters are
increased; the multi-parameter χ2 space contains many local minima and hence the
the fit is very sensitive to the parameter starting points that are chosen. Calculation time
for a many-parameter gradient descent can also be non-trivial. The second problem,
and perhaps the most time consuming, is to construct an accurate estimate of the
systematic uncertainties. This task involves tracking down the measurements used for
the Geant4 Xe(n,n)Xe cross section databases to find the total uncertainties in those
studies. One must then vary the Xe(n,n)Xe cross section database values according to
those uncertainties many times, each time re-running the M.C. simulation and performing
additional best-fits. Additional systematic uncertainties arise due to discrepancies between
the real detector geometry and that which has been coded into Geant4.
96
Best−Fit Leff
10
2
103
104
AmBe DataMonte Carlo
Flat 19% Leff
Cou
nts
Energy [keVee]0 2 4 6 8 10 12 14
102
103
Figure 4-12. Real and simulated spectra of elastic neutron scatters from AmBe in theXecube detector. The dashed lines are the full spectra, while the solid linesindicate the part of the spectra used in the fitting procedure. (Top) The twospectra after varying the Leff spline knots to form a best-fit (χ2/ndf=1.1).(Bottom) The spectra shown after scaling the simulated data by anenergy-independent Leff =0.19 (χ2/ndf=26.3), as used in XENON10.
Despite these difficulties, a best-fit result without the rigor described in the previous
paragraph can still be useful as a consistency check of the coincident beam data. Figure
4-12 compares the real and simulated AmBe spectra, using the flat Leff =0.19 as in
XENON10 [31] (giving χ2/ndf=26.3), and as well the spectra after varying the Leff spline
to obtain a best-fit (giving χ2/ndf=1.1). The four fixed spline knots are located at 4,
10, 15, and 22 keVr, and the fit is performed by comparing the histograms in Figure
4-12 in the range 1-8 keVee. After scaling the raw M.C. data by Leff , the spectrum is
then convoluted with the detector’s energy resolution, and normalized to match the
total number of events as the real data in the fit energy range. The electron-equivalent
energy resolution (σ/µ) is assumed to be proportional to 1/E2, with the constant of
proportionality taken from 57Co’s 122 keV line (9.0%). At each iteration, χ2 is computed,
97
and the spline knots varied according to a gradient descent until the minimum χ2 as been
reached. The results of the fit, shown with the 1-σ allowed region (statistical uncertainties
only) is superimposed with the beam data in Figure 4-11.
4.5 Discussion
The data point from the measurement at 109.5 shows agreement with other
measurements whose high-energy behavior averages out to Leff ≈ 0.19. The result of
the best-fit study between data and M.C. of the AmBe data, while lacking systematic
uncertainties, is consistent with all the Xecube beam data. Below 10 keV, the values
obtained in this work are substantially lower than the central values of Chepel et al. [48],
with a considerable improvement in precision. The central value at 10 keV is consistent
with the lowest-energy data point of Aprile et al. [49], enforcing the accuracy of this
measurement. Unfortunately, the theoretical models of neither Lindhard [46] nor Hitachi
[45] can shed any light on the behavior of Leff in this energy range. Hitachi’s model,
which attempts to take into account incomplete charge recombination and additional
electronic quenching, is based on Lindhard quenching as well as the Thomas-Fermi
approximation; for Xe nuclear recoils, both break down below 10 keV [90, 91].
As mentioned in the introduction, the uncertainty in Leff at low recoil energies
presents the largest systematic uncertainty in the results of the XENON10 dark matter
experiment, where it was chosen to use a flat Leff = 0.19 as a compromise between the
seemingly opposing trends observed by Chepel and Aprile. Under this assumption,
the WIMP-nucleon spin-independent cross section for WIMPs of mass 100GeV/c2 and
30GeV/c2 was constrained to be less than 8.8×10−44 cm2 and 4.5×10−44 cm2, respectively,
indicated by the solid curve in Fig 4-13. Allowing for Leff scenarios below 20 keV that
cover the values allowed by both Chepel and Aprile gives upper limits that vary by
∼40% at 30 GeV/c2 and ∼18% at 100 GeV/c2, with variations becoming less severe with
increasing WIMP mass. With an Leff model that follows the new data points of this
study, the resulting upper limit is shown in Fig 4-13 as the dashed curve. The limit is
98
shifted up to 9.9× 10−44 cm2 and 5.6 × 10−44 cm2 for WIMPs of mass 100 GeV/c2 and 30
GeV/c2, respectively.
WIMP Mass [GeV/c2]
WIM
P−
nucl
eon
cros
s−se
ctio
n [c
m2 ]
101
102
103
10−44
10−43
10−42
Figure 4-13. The upper limit on the WIMP-nucleon spin-independent cross section basedon the 58.6 live days of XENON10’s WIMP search, shown with a flatLeff = 0.19 (solid). An Leff function consistent with the results of this study,applied to the same XENON10 data is shown as well (dashed).
It has become clear from XENON10 that future dark matter searches using LXe
must have sensitivity to nuclear recoils below 10 keV in order to be competitive. The
improved understanding of Leff ’s behavior presented in this study not only permits
a more precise interpretation of XENON10’s results, but benefits future dark matter
searches also using LXe. Several next generation LXe dark matter searches are currently
in operation or under construction, such as XENON100 [92], LUX [93] and XMASS [94].
These experiments will begin to probe for the first time those regions of parameter space
most favored by many theoretical models, and will consequently rely quite heavily on a
99
precise understanding of LXe’s scintillation efficiency for low energy nuclear recoils when
interpreting their results. This is true in the case of a null result and especially in the
case of a positive signal. If and when such a signal is detected, a measurement of the
WIMP mass, for example, which relies on analyzing the energy spectrum of recoils, will be
affected by the precision to which Leff is known.
100
CHAPTER 5THE XURICH DETECTOR
Strange how much human accomplishment andprogress comes from contemplation of the irrelevant.
-Scott Kim
A small LXe prototype detector has been constructed at the Universitat Zurich in
order to test liquid xenon’s response to low-energy ionizing radiation, called the Xurich
detector. This chapter discusses the design and performance of this device, leading to the
next chapter which will present results.
5.1 TPC Design
The Xurich detector is a dual-phase LXe time projection chamber (TPC), shown
schematically in Figure 5-1. The stainless steel (SS) vessel is housed within a vacuum
cryostat with cooling provided via a copper cold finger immersed in liquid nitrogen (see
Section 5.2.2). The temperature and pressure are held constant at 175 K and 1.8 bar
(absolute), respectively, and the detector operated stably for several months at a time.
Xurich’s cylindrical active region, 3.5 cm in diameter and 3 cm in height (80.8 g of LXe), is
defined by a polytetrafluoroethylene (PTFE) cylinder on the perimeter and grid electrodes
above (gate) and below (cathode). A third grid electrode (anode) is located above the
gate grid, with the liquid level lying between the gate and anode grids. Two Hamamatsu
R9869 [85] photomultiplier tubes (PMTs) view the active volume, one from below and one
from above. A total of 1.76 kg is used to fill the stainless steel vessel. A PTFE spill-over
cup surrounds the TPC structure, which fixes the height of the liquid. The LXe removed
for recirculation is taken from this cup, and therefore the liquid level in the TPC cannot
exceed the height of the cup.
The cathode and gate grids apply an electric field of typically ∼1 kV cm−1 which
is used to drift electrons away from an interaction site towards the gate grid. Once the
electrons pass through the gate grid, they arrive at the liquid surface and are extracted to
the gas by an electric field of ∼10 kV cm−1 that then accelerates the electrons through the
101
Stainless steel
LXe 3 cm
3.5 cmGate
Cathode
recirculationPumping,Filling,Cables
PTFE
GXe
Liquidlevel Anode
Top PMT
Bottom PMT
Figure 5-1. Photograph and schematic diagram of the dual-phase Xurich detector. ThePTFE structure holds the PMTs and grid electrodes (see text), defining anactive region 3.5 cm in diameter and 3 cm high. The photograph on top is aview up through the anode grid to the top PMT, while the bottom photographis a side-view of the assembled TPC. Diagram prepared by Teresa MarrodanUndagoitia.
gas until they collect on the anode grid. The high voltage applied to the grids is supplied
by a CAEN model A1526 module. During their transit through the gas, the electrons will
collide with Xe atoms with sufficient energy to produce scintillation light. Therefore, the
typical result of a particle interaction is a prompt scintillation signal (S1) emitted from
the interaction site itself, followed by a delayed scintillation signal (S2) produced as the
electrons travel through the gas under the influence of the extraction field. In this way,
both the scintillation and ionization signals are measured by the PMTs. This technique is
used for charge readout because it provides superior amplification over more traditional
methods [95, 96]. Additionally, the z-position of the event can be inferred from the delay
time between the S1 and S2 signals since the electron drift velocity is well known as a
function of the applied field [54].
102
S1 [p.e.]
Cou
nts
0 500 1000 15000
100
200
300
400
500
600
Figure 5-2. Spectrum obtained from 57Co at zero field with Gaussian fit. The run-averagedlight yield is 6.38 p.e./keV.
The light yield in this case is defined as the number of photoelectrons (p.e.) emitted
from the PMT photocathodes per unit energy, and is customarily quoted based on the
primary emission of 57Co. When Xurich is operated in single-phase mode with the liquid
level above the top PMT, the 57Co source produces ∼10 p.e./keV.
In the dual-phase mode, where the liquid level lies below the top PMT (between gate
and anode grids), scintillation light that reaches the liquid level from below is reflected
or refracted due to the differing indices of refraction between liquid and gas xenon [97].
Though some of the refracted photons may be detected by the top PMT, and some of
the reflected photons detected by the bottom PMT, roughly 35% are lost overall. The
result is a significantly larger S1 signal in the bottom PMT compared to the top (70%
on bottom, 30% on top), and an overall reduced light yield as compared with the value
taken in single-phase mode. The dual-phase 57Co zero-field light yield is measured to
be 6.38 ± 0.05(stat) ± 0.36(sys) p.e./keV, with 11.5% resolution (σ/µ). The systematic
uncertainty is taken from the level of fluctuations in this light yield over time, and the
statistical uncertainty is the combination of fit uncertainties from each 57Co zero-field data
set. The spectrum obtained from one 57Co calibration is shown in Figure 5-2.
103
5.2 Auxiliary Systems
The normal environment of the laboratory is not suitable for operation of a
LXe TPC. Therefore, a set of auxiliary systems are necessary to achieve the desired
temperature, pressure, and chemical purity. These systems, the cryostat and gas handling
system, are described in this section.
5.2.1 Cryostat
Temperature control of the Xurich detector is provided by a vacuum-insulated
cryostat, shown in Figure 5-3, constructed at the University of Florida. A copper cold
finger, also vacuum insulated, is immersed in a liquid nitrogen (LN) bath, at 77K. The
cold finger attaches to the bottom of an aluminum can that in turn attaches at the top to
the stainless steel vessel containing the TPC. The path of heat flow is thus from the SS
vessel to the aluminum radiation shield, from there to the copper cold finger and finally to
the LN bath.
Liquid nitrogen (LN)
PMT SigGrid Voltage
Vacuum pump
Vacuum
GXe
Xe Recirc.PMT HVCathode V
LN emergency loop
Cold finger to LN
Cryostat can
Radiation shieldLXe
Figure 5-3. A photograph and cross-sectional schematic of the cryostat that houses theXurich detector. Cooling is provided by a vacuum-insulated copper cold fingerimmersed in liquid nitrogen.
104
Resistive heaters are also located on the top of the radiation can, and are powered
by a Cryocon model 34 temperature controller [98]. The cryostat in this manner provides
exceptionally stable cooling power, with fluctuations at the level of 0.01–0.1K over months
of continuous operation. Though the normal operating temperature is 180K, the cryostat
is capable of reaching roughly 140K when no heat load is applied. Two temperature
Time [days]
Tem
pera
ture
[K
]
0 5 10 15 20 25150
200
250
300Top of radiation canLXe
Figure 5-4. The cryostat performance over roughly one month. In this plot, the initialliquid nitrogen fill is done at t ≈ 1.5 days, and proceeds for another 1.5 days.The abrupt rise in temperature at t ≈ 3 days corresponds to the heaters beingturned on.
sensors are normally read out, one located on the top of the radiation can, while the other
is located in the LXe. The vacuum in the cryostat space is kept below 10−5 mbar by a
Varian turbomolecular pump.
5.2.2 Gas System
The Xurich detector uses a dedicated gas system that is responsible for Xe filling,
recirculation and purification, recovery, and storage. The frame of the gas system was
built at the University of Florida, while the plumbing was constructed at the Universitat
Zurich using mainly 14in Swagelok connections [99]. A picture of the gas system, and a
schematic diagram, are shown in Figure 5-5.
When not in use, the Xe gas is stored in Cylinder 1. Prior to cooling the cryostat,
the inner LXe space of the detector is evacuated and then filled with 2 bar (absolute) of
105
Filter
meterFlow−
Buffer Rec. pump
Cylinder 1 Cylinder 2
Rb
LXe
Detector
Regulator
Getter
Filter Rb valve
Figure 5-5. The gas system in charge of Xe filling, purification, recovery, and storage. Thearrows indicate the path of the Xe gas during recirculation. Diagram preparedby Teresa Marrodan Undagoitia.
Xe gas at room temperature, that acts as a thermal transfer gas during cool down. Once
operating temperature (175K) has been reached, Xe gas is transfered from Cylinder 1
via the pressure regulator, through the getter and flow meter and into the LXe inner
chamber where it is condensed. Cylinder 2 stores excess Xe and also acts as an emergency
recovery volume in case of any problems during filling. A LN dewar is connected through
an electronic cryogen valve to a copper loop surrounding the radiation can. If the pressure
in the inner chamber exceeds 3 bar, the valve opens automatically, providing additional
cooling power.
The getter uses a heated metal that absorbs electronegative impurities. Once the Xe
filling is complete, the recirculation pump (labeled “Rec. pump” in Figure 5-5) is turned
on and the Xe is directed along the path indicated by the arrows. The flow rate is kept at
8.5 SLM and is controlled by a metering valve, indicated on the diagram as the valve icon
with a diagonal arrow through it, located before the buffer volume. The measurement and
evolution of the LXe purity is discussed in Section 5.6.
106
Xe recovery is performed by cooling Cylinder 1 to 77 K with LN and opening a
path from the Xurich detector to Cylinder 1 that bypasses the regulator. The vacuum
insulation space of the cryostat is simultaneously vented and the cold finger is removed
from the LN bath.
5.3 Photomultiplier Tubes
The PMTs used in the Xurich detector are made by Hamamatsu, model R9869,
shown in Figure 5-6. With the exception of the photocathodes, the two PMTs are
identical in design. The multiplier section consists of twelve stages of a metal channel
dynode structure. The PMT that is placed on the top of the detector, in the gas, has a
new type of photocathode designed to have a quantum efficiency of &35% [85], while the
bottom PMT has a more standard photocathode with quantum efficiency ≈25%. Voltages
are distributed to the cathode and dynode chain by a voltage divider built onto a PTFE
disc substrate.
Figure 5-6. One of the photomultiplier tubes used in the Xurich detector. Thephotocathode is facing down, and visible is the initial test voltage divider.
The gain of the PMTs is calibrated with a pulsed blue light emitting diode, in a
process explained in Chapter 7. The single p.e. spectra obtained from these PMTs at
varying applied voltages is displayed in Figure 5-7. Also shown is the behavior of the
107
750 V
100
101
102
103
104
105
800 V
Gain×10
Cou
nts
850 V
−0.5 0.5 1 1.5 2
x 108
100
101
102
103
104
900 V
−0.5 0 0.5 1 1.5 2 2.5
x 108 PMT Voltage [V]
PMT
Gai
n
650 700 750 800 850 900 9500
1
2
3
4
5
6
7x 10
6
SPE
Res
olut
ion
(σ/µ
)
0.4
0.5
0.6
0.7
0.8
0.9
1GainResolutionPMT 1PMT 2
Figure 5-7. Single photoelectron spectra from Xurich’s photomultiplier tubes at varyingapplied cathode voltages. In each panel, the red histogram is from the topPMT, while the blue histogram is from the bottom. The extracted gain andsingle photoelectron resolution is also shown.
gain and single photoelectron resolution as a function of applied voltage. The operating
voltages used for the two PMTs—900V for PMT1 and 850V for PMT2—are supplied by a
NHQ 225M NIM module and are chosen to minimize the resolutions while nearly equating
the gains.
5.4 Data Acquisition and Signal Processing
5.4.1 Hardware
The raw PMT signals are fed to an external fast voltage amplifier (Phillips 777),
or when no external gain is needed, to a linear fan-out (CAEN N454). Both units have
two outputs; one output is connected directly to the analog-to-digital converter (ADC),
Acqiris model DC436 100MS/s, while the other output is fed to the triggering system.
A CAEN N840 leading edge discriminator provides a channel-by-channel trigger whose
threshold is set at ∼1.5 p.e.. These logic signals are then timed by a N93B timing unit so
that each pulse lasts 10 µs. The timed signals are connected to a N455 coincidence unit set
to ‘AND’ (requiring coincidence in the two PMT channels), and this signal then functions
as the trigger for the ADC. The trigger setup is shown schematically in Figure 5-8. The
ADCs are outfitted with internal bandwidth filters that suppress signal components with
frequency larger than 50MHz, to avoid Nyquist aliasing.
108
ADC
Cryostat
PMT 1
PMT 2
Amp/FAN
Discrim Timer
Ch 1 Ch 2 Trig
AND
Xe
Figure 5-8. Schematic of the data acquisition system
The efficiency of the trigger is studied by two methods. The first method involves use
of a 137Cs which gives a 662 keV γ-ray. This source is used because at the low energies its
Compton spectrum is featureless and flat; indeed, it is the same source used to calibrate
the ER band in the XENON10 experiment, described in Section 3.1.3.
The second method used to study the efficiency is by constructing a Monte Carlo
simulation (MC). The MC begins by simulating realistic PMT response, described later in
Section 7.2, in order to determine the efficiency to catch N p.e. given a trigger threshold
of 1.5 p.e.. Next, the combination of geometrical light collection efficiency, quantum
efficiency, and 1st dynode collection efficiency, εtot, is estimated from,
εtot = Lp.e.Wph(β), (5–1)
where Wph(β) = 21.6 eV [100] is the energy required for a recoiling electron to produce
a single scintillation photon in LXe at zero applied field, and Lp.e. = 6.74 p.e./keV is
the measured light yield of Xurich at 9.4 keV (see Table 6-1). From the detected signal
reaching the PMTs, 30% is detected in the first PMT (top), while 70% is detected in
the second PMT (bottom). The individual PMT efficiencies for detecting an initial
scintillation photon, ε(1,2), are therefore ε(1) = 0.3εtot and ε(2) = 0.7εtot. The MC starts
109
with an initial number of scintillation photons, Ninit, and simulates a number of p.e. for
each PMT, N(1,2)p.e. , by choosing a random integer from a binomial distribution with Ninit
trials and ε(1,2) probability of success. The efficiency to catch N(1,2)p.e. p.e. given a trigger
threshold of 1.5 p.e. is then applied, and coincident positive detection by both channels
required. The procedure is repeated 103 times for each Ninit ∈ [1, 700] The simulated
S1 [p.e.]
Cou
nts
0 20 40 60 80 10010
0
101
102
103
Trig
ger
Effi
cien
cy
10−0.6
10−0.4
10−0.2
100
100.2
Figure 5-9. Study of the trigger efficiency of the Xurich detector, given individual PMTtrigger thresholds of 1.5 p.e.. The spectrum of 137Cs is in blue, while theefficiency from the Monte Carlo simulation is given in red.
trigger efficiency is shown in Figure 5-9 in red, along with the real 137Cs data. The results
show ∼95% efficiency at 20 p.e., rolling down to ∼70% at 10 p.e. and ∼10% at 5 p.e..
5.4.2 Software
XeDaq, a LabVIEW [101] program constructed specifically for the Xurich Acqiris
ADCs, is run on a PC and communicates with the ADCs via a CompactPCI (cPCI)
connection. The vertical resolution of the Acqiris is 12-bit and the samples are stored as
short integers and transfered directly to disk with 1000 events per file. The processing
procedure occurs in three steps: preliminary data manipulation, S2 finding, and S1
finding.
110
5.4.2.1 Preliminary data manipulation
The preliminary data manipulation begins by finding the baseline level for each
channel, taken as the average value of the first 100 samples in a trace. This value is then
subtracted from the entire trace (channel-by-channel and event-by-event). A copy of each
trace is made that has been ‘flattened’. That is, any sample whose value lies within 6
bins of the baseline is set to zero. This flattened data is used only in the pulse finding
algorithms and is not used in the calculation of pulse areas. The next step involves unit
conversion; the initial unit of the sample value is simply bins, corresponding to a number
between 0 and 4095 (212 − 1). As this is not very useful for subsequent analysis, the results
of the most recent PMT gain calibration are used to convert the sample values from bins
to p.e./sample. With this step complete, any sum over samples will result in a value in
p.e.
5.4.2.2 S2 finding
The next step, S2 finding, is the most computationally intensive process. This
algorithm is charged with distinguishing between S2 from S1 pulses, computing S2 pulse
areas, and determining the timing parameters. This is a difficult task, because S2 pulses
often appear irregularly shaped, seen in Figure 5-10 (top). Additionally, some small S2
events are not a characteristic ‘pulse’, but instead a series of small pulses spread out over
∼1µs, as seen by the signal in the inset plot.
The S2 finding algorithm takes advantage of the fact that, though oddly shaped, S2
pulses always occur over a span of ∼1µs, while S1 pulses are no wider than hundreds of
ns. First, a ‘S1-like’ box area, A(1)i , is computed,
A(1)i =
i+N1/2∑
m=i−N1/2
Sm, (5–2)
where Sm is the mth sample value (summed over all PMTs) from the flattened data, and
N1 is the S1 box width, set here to 150 ns, characterizing the largest S1 peak widths.
When m is either negative or greater than the trace length, Sm is considered to be
111
t [µs]
p.e.
/sam
ple
0 5 10 15 20 25
0
20
40
60
80
100
t [µs]
p.e.
/sam
ple
10.5 11 11.5 120
0.5
1
1.5
2
2.5
S1
S2
S2
t [µs]
p.e.
/sam
ple
0 5 10 15 20 25
0
2
4
6
8
10 S
i
A (2)i
Figure 5-10. (Top) An example raw PMT output trace from an event in dual-phase mode.The inset box shows a zoomed view of the small S2 pulse enclosed by theblack dashed box. (Bottom) The same trace, with a zoomed vertical axis, andthe result of the S2 filter in red. The filter has managed to respond to thelegitimate S2 pulses, while remaining unaffected by the S1.
identically zero. Next, a filtered signal is created by calculating a ‘S2-like’ box filter,
similar to A(1)i , and subtracting the value of the largest A
(1)i that lies within the S2 box:
A(2)i =
i+N2/2∑
m=i−N2/2
Sm −max[A(1)j ], j ∈
[i− N2
2, i +
N2
2
], (5–3)
where N2 is the S2 box width, set to 1.4 µs. In this way, if the area inside the S2-box is
concentrated within a small time window, A(2)i will be close to zero. The output of this S2
filter is shown in Figure 5-10 in red, superimposed over the real trace.
Once this filtered signal has been computed, free of any S1 contribution, it is used
to find the position and widths of the S2 pulses. The pulse finding algorithm here is
quite simple; it takes the maximum value of A(2), and steps iteratively to the left until
A(2) reaches zero. The extent of the pulse to the right is likewise found. The area in this
window is then computed from the sum of the original (unflattened) traces. The values
112
of A(2) and Sm are then set equal to -0.1 p.e. within the pulse bounds, and the process is
repeated two more times. A value of -0.1 p.e. is chosen so that the locations of S2 pulses
can be easily identified in the next step.
5.4.2.3 S1 finding
At this point, the flattened traces have had S2 pulses removed, and what remains
is only S1 pulses. The algorithm for finding S1 pulses from the flattened trace (summed
over all PMTs) is the same as that which finds S2 pulses from A(2). However, once a pulse
is found, it must meet two requirements before it is considered a legitimate S1. First,
the pulse must exist in both PMTs, in coincidence such that both PMTs show at least
one p.e. within the pulse window. Next, the trace must be ‘clean’ before and after the
pulse. This means that Sm = 0 for three samples before and after the pulse bounds. This
constraint is made for two reasons. First, it eliminates pulses that are surrounded by
excess noise. Second, some large S2 pulses will incite after-pulsing in the PMTs for the
span of several µs; this after-pulsing sometimes does not produce a response in A(2), and
therefore remains in Sm, possibly mimicking a S1 signal.
5.5 Liquid Level
The electrons that have drifted away from the interaction site and cross the liquid
surface produce the S2 scintillation light during collisions with Xe atoms in the gas phase.
The gas gain, the number of photons produced per electron, depends on the conditions
that the electrons experience in the gas. Namely, the gas gain is dependent on the electric
field in the gas, the gas density, and the distance traveled through the gas. The first
should be the same in all regions of the gas gap. However, the second and third can
exhibit non-uniformity. Though the voltage difference between the gate and anode grids
is uniform, and the distance between these grids is uniform, the liquid level might not be,
due to an overall tilt in the device. Because the dielectric constant of LXe is roughly a
factor of 2 greater than that of GXe, this means that the field in the gas, Eg, depends on
113
the liquid level as,
Eg =Vgate
d− h/2, (5–4)
where Vgate is the potential difference between gate and anode, d is the spacing between
gate and anode, and h is the level of the liquid above the gate grid. The gas gain, nph, is
given by [95],
nph = 70(Eg/p− 1.0)xp, (5–5)
where Eg is in kV cm−1, p is the gas absolute pressure in bar, and x is the gas gap in cm
(x = d − h). Figure 5-11 shows the gas gain as a function of gas gap for a fixed set of p,
Vgate, and d.
Gas Gap [cm]
S2 G
ain
(Bol
ozdy
nya)
0 0.1 0.2 0.3 0.4 0.50
50
100
150
Figure 5-11. The S2 gain, calculated after [95] as a function of gas gap, for a fixedVgate = 3 kV, p = 1.8 bar, and gate-anode spacing d = 5 cm.
If an overall tilt in the device exists, this means the S2 gain from one location of
the detector will be different than in other regions, and will degrade the resolution of
the ionization signal. It is therefore necessary to ensure the liquid surface is as close as
possible to being parallel with gate and anode grids.
In order to test the liquid level, the localized energy deposition of γ-rays from
57Co is employed. Data are taken with the source placed on the cryostat body at four
different azimuthal (θ) positions, all at the same height z. Assuming the drift field, Ed, is
114
uniform in θ, then the absolute charge collected from the interactions should be constant
throughout the data taking. Although extrapolation of the absolute number of photons
emitted is difficult, the position of the peaks in the S2 spectra give an indication of the
relative liquid level. Figure 5-12 shows the S2 spectra and peak positions for data taken at
four source positions.
x01_20090811T1450 − back position
0 0.5 1 1.5 2 2.5 3
x 105
0
100
200
300
400x01_20090811T1458 − right position
0 0.5 1 1.5 2 2.5 3
x 105
0
100
200
300
400
S2 [p.e.]
Cou
nts
x01_20090811T1508 − front position
0 0.5 1 1.5 2 2.5 3
x 105
0
100
200
300
400x01_20090811T1528 − left position
0 0.5 1 1.5 2 2.5 3
x 105
0
100
200
300
400
Source Angular Position [deg]
S2 m
ean
[p.e
.]
0 50 100 150 200 250 3005
5.5
6
6.5
7
7.5
8
8.5x 10
4
Figure 5-12. (Left) The S2 spectra from 57Co taken at various azimuthal positions beforeleveling the detector. (Right) The position of these S2 peaks as a function ofsource azimuthal coordinate.
Source Angular Position [deg]
S2 m
ean
[p.e
.]
0 50 100 150 200 250 3005
5.5
6
6.5
7
7.5
8
8.5x 10
4
S2 [p.e.]
Source at 270o
0 0.5 1 1.5 2
x 105
0
100
200
300
Gaussfit meansHistogram peak pos. at 270 deg
Figure 5-13. The S2 peak positions after performing leveling, confirming consistency. Thepeak position at 270, determined by a Gaussian fit, is displaced from theposition of the maximum histogram bin due to a non-negligible skew in thespectrum (inset). The position of the maximum bin is indicated by the red×.
115
While the data indicate a gradient in the gas gain pointing roughly towards 0, it
is impossible to tell from these data exactly how much the detector is tilted. In order
to estimate this, a standard bubble-level is placed on the top portion of the cryostat
frame, and the leveling rods adjusted accordingly. Following this procedure, the 57Co
measurements are repeated. Figure 5-13 shows the S2 peak positions after leveling.
With the exception of the point at 270, the positions are statistically consistent. The
S2 spectrum taken at 270 (Figure 5-13, inset), unlike the other three positions, shows
a pronounced skew, and the peak position of the Gaussian fit is considerably displaced
from the peak bin in the histogram. The red ‘×’ indicates the position of the maximum
histogram bin, which appears to now be consistent with the other angles.
5.6 LXe Purity and Electron Lifetime
As electrons leave the interaction site, they travel through the liquid under the
influence of the drift field, Ed. In order to be detected, they must arrive at the gas gap
unimpeded, however, several possible electronegative impurities can act as attachment
sites for the drifting electrons, removing them from the detected signal. The rate constant
for attachment to O2, N2O, and SF6 as a function of applied field is shown in Figure
5-14 [102].
Although SF6 clearly shows the strongest effect, the most import of these three
impurities to Xurich is O2, as the system is first exposed to room air. The metal getter is
particularly good at removing O2, however, and the effectiveness of recirculation can be
readily seen by measuring the purity over time.
The level of purity is determined by monitoring the parameter known as the electron
lifetime, τ . Given a known (or at least uniform) amount of charge emitted from an
interaction, the amount of charge reaching the gas gap, Q(t) given an initial amount Q0
follows an exponential decay as a function of the drift time (the time between S1 and S2),
as,
Q(t) = Q0e−t/τ . (5–6)
116
electric field strength [ Vcm−1 ]
k (e
− +
S)
[ M−
1 s−
1 ]
O2
N2O
SF6
101
102
103
104
105
1010
1011
1012
1013
1014
1015
Figure 5-14. The rate constant for attachment of electrons for three different impurities inLXe as a function of applied field. Figure taken from [102].
The measurement of τ is accomplished by measuring the S2 peak in the 57Co
spectrum as a function of drift time. Figure 5-15 shows a plot of S2 versus drift time
at the beginning of the run (left) and again after approximately one week of recirculation
(right). The vertical axis is given as the natural logarithm of the S2 size, and hence the
slope of the band gives τ . The progression of the measured electron lifetime as a function
of date is shown in Figure 5-16. Although a value is reported for the later data sets, the
data from Figure 5-15 (right) are statistically consistent with zero slope, and hence the
reported lifetime is a lower limit. The maximum drift time is 15-20 µs (depending on the
drift field), and thus a characteristic lifetime of &300µs ensures less than 5% charge loss
from events occurring at the bottom of the detector.
The electron lifetime, τ , can be used to find the concentration of impurities, typically
given in ‘O2 equivalent’. The concentration of free electrons, Ce− , follows the relation,
dCe−
dt= −knCe− − krCe−CXe+ − kO2Ce−CO2 , (5–7)
117
Drift Time [µs]
log(
S2[
p.e.
])
0 5 10 150
2
4
6
8
10
12
14
16
Drift Time [µs]
log(
S2[
p.e.
])
0 5 10 150
2
4
6
8
10
12
14
16
Figure 5-15. S2 versus drift time from 57Co taken at the beginning of the run (left), andafter approximately one week of purification (right).
Day in May
Ele
ctro
n Li
fetim
e [µs
]
0 1 2 3 4 5 6 710
−1
100
101
102
103
Figure 5-16. The measured electron lifetime over the course of one week of xenonrecirculation.
where CXe+ is the concentration of Xe ions, CO2 is the concentration of dissolved O2,
and kn,r,O2 is the rate constant for neutralization, recombination, and attachment to O2,
respectively. The attachment term dominates by several orders of magnitude over the
neutralization and recombination terms, and can be neglected for drifting electrons [102].
The concentration of electrons is then given by,
Ce−(t) ∝ exp(−kO2CO2t) . (5–8)
118
Equating the exponents of Equations 5–6 and 5–8 gives,
CO2 =1
τkO2
. (5–9)
With kO2 taken from Figure 5-14, CO2 is in units of mol/m3 (molar). Using kO2 ≈7 × 1010 M−1 s−1, the concentration of O2 at the beginning and end of purification (from
Figure 5-16) is 182 ppt and 0.794 ppt (g/g), respectively.
119
CHAPTER 6LIQUID XENON CALIBRATION WITH 83RB
One thing I have learned in a long life: that all ourscience, measured against reality, is primitive and
childlike—and yet it is the most precious thing we have.
-Albert Einstein
6.1 The Need for a New Calibration Source
Due to varying responses of LXe to different types of particle interactions, it is
necessary to calibrate a detector with a source whose response is known relative to the
particles under study. One common such “reference source” is 57Co, which emits γ-rays
predominantly at 122 keV.
Dark matter direct detection experiments search for low energy nuclear recoils caused
by the scattering of WIMPs with atomic nuclei. There are two main problems involved
in using 57Co to calibrate LXe detectors for this application. The first is that the γ-ray
energy is much higher than the recoiling nuclei energy produced by WIMP interactions.
Second, the attenuation length of 122 keV γ-rays in LXe is ∼2.5mm, and hence the
energy deposition will be highly localized as compared with the tens of cm typically
characterizing the size of such detectors. The two problems are actually compounded,
because the attenuation length of γ-rays decreases as their energy decreases, and therefore
sources providing lower-energy γ-rays will give an even more localized response than 57Co.
The topic of localization is an issue for point sources placed outside the detector, but
also for point sources placed inside the detector. In the latter case, the source must be
attached to a mounting device of some kind; for low energy γ-ray sources, any device used
for this purpose will likely block some of the scintillation light and potentially distort any
existing applied electric fields. It is therefore not possible to calibrate a detector with
an internal point source under the same conditions that would exist during the actual
measurement. To avoid these difficulties, short-lived noble gas sources can be used which
diffuse uniformly in LXe. The XENON10 experiment used the metastable 131mXe [31, 103].
120
This source solves the second problem (spatial uniformity), but its 164 keV transition does
not overcome the problem of an appropriate energy scale. Additionally, due to its half-life
of twelve days, the detector must sit for approximately 2.5months following a calibration
until the source activity has dropped to 1% of its initial value.
A promising alternative solution is to use the metastable 83mKr, first proposed in
[104]. This source has been used for calibrations of detectors in the Large Electron-Positron
Collider [105, 106], as well as in the KATRIN experiment which attempts to measure the
electron neutrino absolute mass [107]. 83mKr should diffuse uniformly in a LXe detector,
addressing the issue of spatial uniformity. Additionally, its two de-excitation lines at
9.4 and 32.1 keV lie in the energy range of interest for dark matter direct searches, and
its half-life of only 1.8 hours allows for a short turnaround time following measurement.
This chapter presents a successful implementation of this calibration source in the Xurich
detector. Furthermore, results of measurements of the LXe energy scale linearity, evolution
of energy resolution with energy, effects of LXe response under applied electric fields are
shown, and limits on the level of long-lived radiocontaminants introduced by this method
are set.
6.2 The 83mKr Source
83mKr is produced by the decay of 83Rb via pure electron capture. This process
leaves the nucleus in any of 83Kr’s many excited states lying below the Q-value of the
Rb decay (910 keV). Regardless of the initial krypton excited state, the nucleus rapidly
de-excites within picoseconds to the second excited state, isomeric 83mKr, located 41.5 keV
above the ground state. Isomeric krypton decays with a half-life of 1.83 h to the first 83Kr
excited state (9.4 keV), which then decays to the ground state with a half-life of 154 ns [57].
The decay scheme of 83mKr is shown in Figure 6-1, indicating that most of the released
energy is carried by internal conversion and Auger electrons [106]. The 6 kBq 83Rb source
used in this study was produced at the Nuclear Physics Institute, Rez (Czech Republic).
This institute also provides 83Rb for the KATRIN experiment [107]. The parent 83Rb is
121
83Kr
83mKr
IC(30 keV)+A(2 keV)
IC(18 keV)+A(10 keV)+2×A(2 keV)
IC(18 keV)+X(12 keV)+A(2 keV)
76%
9%
15%
IC(7.6 keV)+A(1.8 keV)
γ(9.4 keV)95%
5%
32.1 keV(1.83 h)
9.4 keV(154 ns)
Figure 6-1. The decay scheme and branching ratios of 83mKr. The decay always passesthrough two transitions, giving mostly internal conversion (IC) and Auger (A)electrons. A small amount of the energy is carried by gamma-(γ) and X-rays(X) [106] (the distinction between γ- and X-rays is in their source: γ-rays arephotons emitted by nuclei, X-rays are photons emitted by electrons).
produced in the U-120M cyclotron from the reaction natKr(p,xn)83Rb by irradiating a
medium-pressure gaseous krypton target with 27 MeV protons. The product, deposited
on the target chamber walls, is then washed into several tens of milliliters of high purity
water (<0.07µS/cm). An appropriate amount of the target eluate is then absorbed in
zeolite beads (2 mm diameter, Merck), which acts as a molecular sieve. Zeolite was chosen
due to its ability to allow for efficient emanation of 83mKr in vacuum, while exhibiting high
retention of the mother 83Rb in its porous structure. The details of the source production
process are described more thoroughly in [108]. In addition to 83Rb, 84Rb (t1/2=38days)
and 86Rb (t1/2=19days) are also produced, however, they decay to stable Kr isotopes
and hence introduce no radioactive backgrounds. Since 83Rb decays with a half-life of
86.2 days, the source strength decreased to ∼3 kBq by the end of these measurements.
83mKr is introduced into the flow of the closed recirculation circuit by means of a
single port with a valve. The zeolite beads containing the 83Rb reside in a small chamber
filled with the same xenon gas that flows in the gas system. Gaseous 83mKr emanating
from the 83Rb decay may then diffuse into the recirculation circuit, its introduction being
easily controlled by either opening or closing the valve at the port, denoted as the Rb
valve. Due to the rather long half-life of 83Rb (86.2 d), it is imperative that no trace of this
122
mother radionuclide enters the system if it is to be used in a low background experiment.
Rb might potentially enter the system by one of two ways: as a vapor, which is very
unlikely since its volatility under common laboratory temperatures even under vacuum is
not significant; or as an aerosol formed from small particles of the zeolite itself. Aerosol
breakthrough is not entirely excluded, and therefore a 0.5 µm aerosol filter is placed
between the Rb chamber and the Rb valve in order to prevent any 83Rb from entering the
recirculation loop. Measurements done to assess the level of 83Rb introduced in the the
system are discussed in sections 6.3 and 6.4.
6.3 Analysis and Results
Once the 83mKr has entered the LXe, a 32.1 keV transition might occur in the active
region, which will then be followed by the 9.4 keV transition. A 83mKr decay is, therefore
indicated by two S1 pulses whose separation in time is characterized by a decaying
exponential with t1/2=154 ns. Some of these transitions will occur too close in time to be
resolved separately, giving a single 41.5 keV pulse; however, the strength of this signal is
well below the background level in the Xurich detector. On the other hand, many of the
83mKr decays have a double S1 structure, while only a small fraction of non-83mKr decay
events share this feature. An example of the PMT response from a 83mKr decay is seen in
Figure 6-2 (top).
The events with such a double S1 structure are shown from one data set in Figure 6-2
(bottom), with the area of the first pulse plotted versus the area of the second pulse. In
this space, it is evident that the 83mKr decays form a population of events that is clearly
separated from background. The box indicates the energy cuts for first and second S1
pulses used to identify 83mKr decays; before opening the Rb valve, background data show
no events within this box. After the Rb valve has been opened, the rate of 83mKr decays
in the total LXe volume increases to the 20 Bq level in roughly 10 h. In order to further
check that these are indeed 83mKr decays, the distribution of S1 delay times (i.e. the
time between the first and second S1 pulses), ∆tS1, of events within the box of Figure
123
t [ns]
p.e.
/sam
ple
0 500 1000 1500 20000
20
40
60
First S1 [p.e.]
Seco
nd S
1 [p
.e.]
Background
0 100 200 300 4000
20
40
60
80
100
120 83mKr
0 100 200 300 400
Figure 6-2. (Top) PMT output from a 83mKr decay. In this double pulse of primaryscintillation light (S1), the first pulse corresponds to the 32.1 keV transitionwith the second pulse resulting from the 9.4 keV transition. (Bottom) The areaof the first S1 pulse versus the area of the second, for events showing thischaracteristic two-pulse structure. Shown are distributions taken before Rbexposure (‘Background’) and during Rb exposure (‘83mKr’), demonstratingthat the population of 83mKr decays is clearly separated from backgroundevents. The box represents the energy cuts used as the 83mKr acceptancewindow.
6-2 (bottom) is fit with a decaying exponential. The result of the fit, shown in Figure
6-3 (top), gives t1/2 = 156 ± 5 ns, consistent with the published value of 154 ns [57].
This excellent agreement validates the claim that these events are indeed caused by
83mKr decays.
Due to the shaping of the PMT signals by the various DAQ components, multiple S1
pulses that are delayed by less than ∼100 ns cannot be separately resolved. Additionally,
the signal is required to be ‘clean’ (i.e. flat baseline) two samples before and after the
124
∆tS1
[ns]
Cou
nts
0 200 400 600 800 1000 1200 1400 16000
50
100
S1 [p.e.]
Cou
nts
1st S12nd S1
0 50 100 150 200 250 30010
1
102
Figure 6-3. (Top) The distribution of delay times between first and second S1 pulses forevents in the 83mKr acceptance window. An exponential fit to the distributiongives a half-life of 156± 5 ns, consistent with the published value of 154 ns.(Bottom) Spectra from the two 83mKr transitions, summed over all runs takenat zero field.
pulse, in order to register as a positive S1 identification during the offline processing of
the data. This makes the efficiency for detecting multiple S1 pulses less than unity for
∆tS1 < 250 ns, as is obvious from Figure 6-3 (top). Therefore, the double S1 selection cut
detects 83mKr decays with an efficiency of approximately 32% under these conditions.
The spectra, in p.e., obtained at zero field from the two transitions of 83mKr are
displayed in Figure 6-3 (bottom). A Gaussian function is fit to each spectrum that is used
to determine the light yield and energy resolution, shown in Table 6-1. As mentioned
in section 6.1, 57Co emits primarily 122 keV γ-rays. However, there is a small additional
contribution from 136 keV. The two lines, however, are not distinguishable from one
another due to the detector’s energy resolution and instead give a single peak, whose
125
Table 6-1. The measured zero-field light yield (L.Y.) and peak resolution (Res.), and fielddependence fit parameters, ai. The row following 41.5 keV gives the chargecollection of the summed signal. Uncertainties shown in light yield arestatistical only; because these two peaks are taken from identical events, theirsystematic uncertainties are highly correlated, and hence do not affect thesignificance of the relative rise in light yield.
E (keV) L.Y.(p.e./keV) Res. (σ/µ) a1 a2 (10−4cm/V) a3
9.4 6.74±0.06 20.0% -0.34±0.06 6±3 132.1 6.43±0.04 14.4% -0.55±0.03 8.3±1.5 141.5 — — 0.39±0.01 13±2 0.10±0.01
123.6 6.38±0.05 11.5% -0.671±0.003 14.0±0.2 1
average energy is 123.6 keV. The measurements suggest a rise in the light yield at lower
energies, consistent with behavior previously observed in LXe [109] and also in the
XENON10 detector [60]. The peak resolutions (σ/µ) are also shown at zero field.
Because LXe detectors typically use an applied electric field in order to extract an
ionization signal, it is interesting to consider what happens to the detector response under
such an applied field. As the applied field is increased, more and more electrons leave
the interaction site, suppressing the recombination process that contributes photons to
the scintillation signal. The result is that both the scintillation and ionization responses
vary strongly with applied field, with the two signals exhibiting anti-correlation. It is
then crucial that the field quenching behavior for any calibration sources be known
quantitatively. Figure 6-4 shows the light yield as a function of applied field, normalized to
the zero field value, of the two 83mKr transitions and the 57Co line.
The time scale of the ionization signal, 1-2 µs, does not permit the two 83mKr transitions
to be resolved separately, and instead the S2 signal contains the combination of charge
emitted from both decays. This 41.5 keV summed-signal ionization yield is also shown in
Figure 6-4 normalized to Q0, the theoretical total amount of initial charge produced prior
to electron-ion recombination. This value is determined by plotting the S1 peak positions
versus the S2 peak positions from data taken at various applied fields. As S1 and S2 are
anti-correlated, these data lie along a line having negative slope, with the line’s intercepts
126
Applied Field [V/cm]
S(E
)/S(
0), Q
(E)/
Q0
0 500 1000 1500 20000
0.2
0.4
0.6
0.8
1
57Co83mKr (32.1 keV)83mKr (9.4 keV)83mKr (41.5 keV, Charge)
Figure 6-4. Field quenching, defined as the light yield of a spectral line divided by thelight yield obtained at zero field, or S(E)/S(0). The level of field quenchingdecreases at lower energies, indicating stronger electron-ion recombinationalong the recoil track. Data collected from 57Co are consistent with thosepreviously reported in the literature [56]. Dashed lines correspond to a fitparameterization described in the text. Also shown is the field-dependentcharge collection of the combination of both 83mKr transitions, Q(E)/Q0; thetwo transitions occur too close in time for their ionization signals to beindividually resolved.
representing the total number of quanta, ions plus excitons (Nion + Nex). For electronic
recoils, the ratio of excitons to ions, Nex/Nion, is taken to be 0.06 [110], and hence Q0 is
94.3% the value of the S2 intercept.
The data are fit with a three-parameter function based on the Thomas-Imel box
model for electron-ion recombination [43], given by
S(E)
S(0),Q(E)
Q0
= a1a2E ln
(1 +
1
a2E
)+ a3, (6–1)
where E is the electric field strength, and S, Q are the scintillation and ionization yields,
respectively. The ai are the parameters of the fit, shown in Table 6-1. Because the
scintillation yields are normalized to the value at zero field, a3 is unity and the function
127
therefore contains only two free parameters for the field quenching data. At decreasing
energies, we observe a consistent decrease in the level of field quenching.
The energy of an event can also be measured by counting the total number of
quanta, Nion + Nex. This is called the combined energy scale (CES), and is constructed
by forming a linear combination of the scintillation and ionization signals, αS1 + βS2,
such that nγ = αS1 and ne = βS2, where nγ and ne are the number of emitted photons
and electrons, respectively. The coefficients α and β can be found from the plot of S1
versus S2 mentioned above, by α = E/(WIS1) and β = E/(WIS2), where E is the
deposited energy, W=13.5 eV is the average energy required to produce a single quanta
(electron or photon) [59], and IS1(S2) is the S1(S2) intercept in units of p.e.. The CES
has the advantage that it is not affected by correlated recombination fluctuations which
dominate the S1 resolution over most energies [43], and hence gives an energy estimate
with better resolution than S1 or S2 alone. For example, the S1, S2, and CES spectra of
the 41.5 keV peak taken at 500 V/cm are shown in Figure 6-5. The S1-only and S2-only
peak resolutions are 14.2% and 20.1%, respectively. The resolution of the CES peak at
this field is 10.0%.
The delay time between S1 and S2 gives the drift time of the electrons, and hence
the z-position of the interaction. One important motivation for using this source is that
it should disperse uniformly in the active LXe volume, providing a spatially-uniform
calibration. The summed z-position distribution of 83mKr events taken at drift fields
from 100-1000 V/cm is shown in Figure 6-6 (top). The observed z-dependent rate is flat
with variations consistent with statistical fluctuations on each bin. With this uniform
calibration, the position-dependence of the detector’s response can be measured and
corrected for. Most of the S1 signal is detected by the bottom PMT, and therefore one
expects to see a light yield that is a monotonically decreasing function of z-position
(i.e. more light is collected from events occurring close to the bottom PMT than for events
close to the top). Figure 6-6 (bottom) shows the light yield of the 83mKr decays at all
128
Energy [keV]
Cou
nts
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70S1S2CES
Figure 6-5. Spectra for 41.5 keV at 500V/cm. The S1, S2, and combined energyresolutions are 14.2%, 20.1% and 10.0%, respectively.
positions along the z-axis between the cathode and gate grids for the data run at 1 kV/cm;
solid lines are the band centroids, shaded bands cover ±1σ. In both transitions, the light
yield at the cathode (bottom of active region) is a factor of 1.3 higher than the light yield
at the gate grid (top of active region).
Although the 83mKr decays away in a matter of hours, the 83Rb will live for nearly
1.5 yr before decaying below 1% of the initial activity. If this technique is to be used in
low-background experiments, it is then imperative that no 83Rb atoms enter the system,
and instead must remain trapped within the zeolite or the filter. In order to test this, the
valve to the 83Rb chamber was closed. The rate of 83mKr decays is expected to decrease
exponentially to zero during the following day; however, if 83Rb has entered the system,
the rate vs. time will behave as an exponential decay with a vertical offset. No such offset
was observed in the 83mKr rate following the closing of the Rb valve. Indeed, 2.5 h of
data collected one day after closing the Rb valve resulted in zero observed events. Were
the valve to be left open, approximately 3000 events would be seen in this time period.
129
Z−position [mm]
Cou
nts
Cathode Gate
0 5 10 15 20 25 3010
1
102
103
Cathode Grid
Gate Grid9.4 keV 32.1 keV
S1 [p.e.]
Z−
Pos
ition
[mm
]
0 50 100 150 200 250−5
0
5
10
15
20
25
30
35
Figure 6-6. (Top) Rate of 83mKr decays as a function of z-position, indicating a uniformconcentration. (Bottom) Measured z-dependence on the light yield from83mKr’s two transitions taken at 1 kV/cm. The solid lines indicated the bandcenters, with ±1σ covered by the shaded areas. Both lines show a light yieldat the cathode that is a factor of 1.3 larger than at the gate grid.
A null observation corresponds to a one-sided 90% confidence Poisson upper limit of
− log(1 − 0.9) = 2.3 events. Therefore, the rate of 83mKr decays can be constrained to be
less than,
2.3 events
2.5 h× 32%= 800 µBq (90% C.L.), (6–2)
in the active region.
130
6.4 Discussion
Testing the low energy response of LXe is generally rather difficult, and therefore
83mKr provides a unique tool for such measurements. The rate of 83mKr decays studied
in this work is quite low as compared with the rate of background events due to natural
radioactivity and cosmic rays. However, the double S1 structure of these decays, and
energy cuts used, enable their measurement in a virtually background-free regime. It is
therefore not necessary to use a low background setup simply to study this weak source.
Simultaneous with this work, a demonstration of 83mKr introduction to a single-phase LXe
chamber by a similar technique has been performed by another group [111].
6.4.1 Light Yield and Field Quenching
The light yield and energy resolution at low energies are of particular relevance
for dark matter direct detection searches. As indicated in Table 6-1, the light yield
increases at low energies. Although an accurate quantitative understanding of this process
is incomplete, the observed behavior can be understood qualitatively in the following
manner. The electronic stopping power of electrons in LXe increases at decreasing
energies [112], and thus the ionization density produced by a recoiling electron increases
along the track, with the highest densities concentrated at the track’s end. Because of
this, the overall ionization density caused by a low energy electron will be greater than
for an electron of higher energy. The electrons and ions produced along the track will
rapidly recombine and produce scintillation photons as the electrons fall to their ground
states. The strength of recombination is correlated with the ionization density, because
the characteristic electron-ion distance is shorter for higher ionization densities. Even at
zero applied electric field, not all of the electron-ion pairs produced will recombine to give
scintillation photons [100]. It is then expected that the zero field recombination is stronger
at lower energies (higher dE/dx), giving a higher overall light yield. This picture is also
consistent with the measurements of the scintillation field quenching, shown in Figure 6-4.
131
In that case, the lower energy recoils exhibit less field quenching, which indicates that the
recombination is stronger at these energies.
6.4.2 Radioactive Background Contamination
The observation of no 83mKr decays, one day following the closing of the Rb valve,
sets an upper limit of 800µBq of residual 83mKr inside the active region of the Xurich
detector. Prior to this, the Rb valve had been opened for a total of 150 hours during the
run. The risk of Rb contamination increases with the amount of time that the valve is
opened, and so this upper limit can be normalized to exposure time (150 h). Moreover,
since the source is exposed to the gas system (and not the detector), the total activity
in the LXe chamber should be independent of the detector size, and should instead
depend on only flow rate and method of deployment. The limit of 800 µBq in the active
region (0.08 kg) can be scaled to the total amount of LXe in the chamber (1.76 kg), and
normalized to the exposure, to give <120µBq/h of residual 83mKr in the whole liquid
volume (assuming the 83mKr concentration outside the active region is uniform and equal
to the concentration inside the active region). The branching ratio of 83Rb to 83mKr is
75%, which means this limit on residual 83mKr is a limit of <160µBq/h of residual 83Rb.
To understand how this upper limit would affect an actual dark matter search, a
300 kg detector with 100 kg fiducial mass is taken as an example. A detector of this
size is typical of the proposed next generation of LXe dark matter searches [113, 114].
An exposure to 83Rb of 10 h would be sufficient, under these conditions, to provide
adequate statistics for such a calibration (∼1000 Kr events/kg). Our upper limit of
83Rb contamination translates to a residual rate of <0.46 decays/kg/day in this 300 kg.
Even if this amount of 83Rb was present in the system, the vast majority of decays would
not introduce dangerous backgrounds. In order for a background event to be ‘dangerous’
(i.e. appear in the WIMP signal acceptance window), it must have two features: (1) it
must produce a single scatter event; (2) the event must deposit a small amount of energy
that is within the WIMP search energy window. An additional feature that dual-phase
132
LXe TPCs have is the ability to reject electronic recoils on an event-by-event basis
at upwards of ∼99.9% based on the ratio S2/S1 (see Figure 3-8). However, statistical
fluctuations can cause a small fraction of electronic recoil events to yield a S2/S1 ratio
similar to values characteristic of a nuclear recoil from WIMPs, and thus the overall
background level must be minimized as much as possible. Any 83mKr decays in the
active volume would not present a problem because they would either have a double
S1 structure (and could be vetoed on that basis), or would give 41.5 keV, outside of the
WIMP search region. The only possibility for a dangerous background is from one of
the γ-rays produced as the initial excited 83Kr decays to the metastable state. These
γ-rays are mostly emitted in the range of 500-600 keV; again, to be dangerous they are
required to single-scatter in the fiducial region, which is highly unlikely given their 3-4 cm
attenuation length. With 83Rb contamination at the level of our upper limit, Monte Carlo
simulations indicate that 0.46 decays/kg/day would contribute less than 67 µDRU of
single scatters in the WIMP search energy region (1 DRU≡1 event kg−1 day−1 keV−1). The
projected γ background rate in [113] and [114] due to natural radioactivity in the detector
materials alone is roughly 1mDRU, fully fifteen times greater than our upper limit on the
83Rb background.
6.4.3 Other Contaminants
After a calibration with 83mKr, the stable 83Kr will remain in the system indefinitely
unless some action is taken to specifically remove it. However, the amount of Kr remaining
from a 10 h exposure as described above will be miniscule; less than 106 atoms total, which
corresponds to a concentration of roughly 1 part in 1021 for 300 kg of Xe. Even if this
remaining concentration was higher, Kr will not adversely affect detector functions. The
transport of electrons through the Xe will not be diminished since Kr is chemically similar
to Xe. Additionally, Kr does not absorb Xe scintillation light [115] and therefore will not
impede light collection.
133
In addition to 83Rb contamination, water and oxygen trapped in the zeolite might
also enter the system. While these elements do not pose a problem in the context of
radioactive background, they could affect the charge collection and light yield. Before the
Rb valve was initially opened, the Rb chamber was evacuated to the level of 10−6 mbar
with a turbomolecular pump at room temperature. The Rb valve was then open
continuously for approximately four days, following which diminished charge collection
was observed. The Rb valve was then closed and the purification system allowed time
to restore the LXe purity to a level adequate for negligible charge loss. In subsequent
measurements, the Rb valve was toggled in cycles of 20 h open, 4 h closed, with charge
collection periodically monitored; no charge loss was measured under these conditions.
It is likely that the impurity content in the zeolite was depleted in the initial four days
of exposure, and had left the system by the time the cycles of 20 h exposure began. In
a subsequent run, the Rb chamber was baked for 24 hours at 120C prior to exposure,
following which no effect on the electron lifetime was observed. At no time was any effect
on the light collection seen.
6.5 Exciton to Ion Ratio
The method used in Section 6.3 to determine Q0 is chosen only so as to facilitate a
way to set a “standard” charge scale. The value of Nex/Nion = 0.06 is the theoretical
value based on absorption spectra of solid xenon. However, efforts to actually measure this
quantity have not confirmed this result. In [100], the authors measured 1 MeV conversion
electrons in LXe and determined Nex/Nion = 0.20.
In order to obtain Nex/Nion = 0.20, the authors of [100] used two measurements.
The first measurement is of the zero-field reduction factor, η, defined as the scintillation
efficiency relative to that of relativistic heavy ions. It assumes the reduction in scintillation
yield is due entirely to escaping electrons, and is related to Nex/Nion by,
η = 1− χ
1 + Nex/Nion
, (6–3)
134
where χ = Nion0/Nion, with Nion0 being the number of electrons escaping recombination at
zero field. The measurement (for 1MeV electrons in LXe) is reported as η = 0.64 ± 0.03;
this single measurement does not determine χ or Nex/Nion individually, but constrains
them to lie along a line in the χ–Nex/Nion parameter space. The second measurement
is based on the relationship between scintillation and ionization signals at applied fields
ranging from zero to 13 kV cm−1, and uses the relationship between the normalized signals
as,
S(E)
S(0)=
1−Q(E)/Q0 + Nex/Nion
1 + Nex/Nion − χ. (6–4)
The values χ and Nex/Nion are then determined by maximum likelihood.
χ
Nex
/Nio
n Allowed by η
Allowed by
field−dependence
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 6-7. Constraints on Nex/Nion and χ (≡ Nion0/Nion) based on the data presented in[100]. Shaded areas represent the allowed regions at the 1-σ level. The green+ is the best fit of the blue region.
There are two problems with the methods used. First, although the value of η is
defined relative to the scintillation yield of relativistic heavy ions, the authors have
neglected the uncertainty in the scintillation yield of these heavy ions. Including this
additional uncertainty changes the overall error bar by 30%, so that the true measurement
135
should be reported as η = 0.64 ± 0.04. The second problem is more significant. The
constraints on χ and Nex/Nion based on the scintillation-ionization relationship (Equation
6–4) are stronger than those based on η (Equation 6–3), because there are multiple
data points that can be considered. Oddly, the authors discard more than half of
the data points with no justification for doing so. They speculate that the neglected
data points are inconsistent with the result because of possible amplifier non-linearity.
This is curious, because most of the data do not exhibit any such nonlinearity. More
importantly, neglecting the points as they have done is the only way that this method
can be made consistent with the constraints based on η. If instead one considers all their
data that show linearity in S1 versus S2, the constraints on χ and Nex/Nion are in fact
inconsistent with the η measurement. These constraints are shown in Figure 6-7. The
shaded areas represent the 1-σ allowed region by both methods. The authors do not
report the uncertainties in the field-dependence measurements; these uncertainties have
been estimated based upon the level of fluctuations in the data points, and hence the
shaded-blue region may be an inaccurate representation of the 1-σ error. The best fit here
gives χ = 0.224± 0.027 and Nex/Nion = 0.295± 0.021.
A very similar approach can be made from the Xurich data of the 41.5 keV line. In
this case, instead of using a given value of Nex/Nion to determine Q0, the value of Q0 is
measured and used to determine Nex/Nion. Q0 is taken to be Qmax = limE→∞
Q(E). The
common approach to this problem (and is what was used in [100]) is performed by making
the inverse of Figure 6-4, that is, plotting Q−1 versus E−1 and extrapolating to the vertical
intercept, seen in Figure 6-8. The red line is the same fit that was determined in Table
6-1. The model itself gives the maximum charge collection as Qmax = a1 + a3. The
assumption, then, is that Qmax = Q0 (arising from Nion), and that any scintillation light
remaining after this value is the result of Nex. Also shown in Figure 6-8 is the expected
Qmax if Nex/Nion is 0.06 and 0.20.
136
E−1 [cm/V]
Q−
1 [p.e
.−1 ]
Nex
/Nion
= 0.20
Nex
/Nion
= 0.06
0 0.005 0.01 0.015 0.020
0.5
1
1.5x 10
−4
Figure 6-8. The inverse charge collection versus the inverse applied electric field of the41.5 keV line. The plot is used to estimate the maximum charge collection (atE−1 = 0). The red line is the same fit given in Table 6-1, but scaling out Q0.Shown are what the vertical intercept should be if Nex/Nion is 0.06 (brownline) and 0.20 (light-blue line).
Figure 6-9 shows S1 versus S2, both scaled to number of quanta, for fields ranging
from 0.1–1.0 kV cm−1. The vertical intercept, IS2, is assumed to be given by Nex + Nion.
Then the ratio of excitons to ions is given by,
Nex
Nion
=IS1
Qmax
− 1, (6–5)
which gives Nex/Nion ≈ 0.96. This value seems quite large, considering the predicted
value of 0.06, however alternate studies find results that similarly differ from prediction. In
[116], a new model for electron-ion recombination studied in conjunction with data taken
from a similar LXe prototype detector indicated values of Nex/Nion ≈ 0.90 for nuclear
recoils.
The Xurich result is not sensitive to χ because S1 and S2 have not been scaled to
S(0) and Q0 as done in [100]. The value of Nex/Nion from both Xurich and [100] depend
137
S1 [photons]
S2
[ele
ctro
ns]
0 500 1000 1500 2000 2500 3000 35000
500
1000
1500
2000
2500
3000
350083mKr 41.5 keVSlope = −1Extrapolated S2
max
Figure 6-9. S1 scaled to photons, versus S2 scaled to electrons, for fields ranging from0.1–1.0 kV cm−1. The vertical intercept is taken as Nex + Nion, while theextrapolation of Qmax is indicated by the black-dashed line.
strongly on how the extrapolation to Qmax is done. The model from Equation 6–1 might
not hold to very high values of the applied field, and hence Qmax could deviate from a1 +
a3. Additionally, it is assumed that the efficiency for excitons to yield scintillation photons
is the same as that for recombining ions. If, for example, the scintillation efficiency for
recombining ions is less than that for excitons, then the horizontal and vertical intercepts
of Figure 6-9 do not represent Nex + Nion, and the value of Nex/Nion extracted here is
artificially too high. The discrepancy between theory and measurement of Nex/Nion can
therefore not be resolved without first, a more robust method of extrapolating Qmax, and
second, a measurement of the efficiency for recombining ions to give scintillation photons.
138
CHAPTER 7PMT STATISTICS
It doesn’t matter how beautiful your theory is, itdoesn’t matter how smart you are. If it doesn’t agree
with experiment, it’s wrong.
-Richard Feynman
If the facts don’t fit the theory, change the facts.
-Albert Einstein
The results presented in the preceding chapters all made use of one particular
scientific instrument, the photomultiplier tube (PMT). This device detects light by a
combination of photoelectric and Auger processes. A general schematic of a PMT is
shown in Figure 7-1. The components reside inside a vacuum chamber to allow the free
Figure 7-1. Schematic diagram of a photomultiplier tube. Figure reproduced withpermission from Hamamatsu Corporation from [117].
transit of electrons. Photons enter the chamber through a transparent window and are
incident upon a semi-transparent photocathode where they emit electrons through the
photoelectric effect. These photoelectrons are accelerated by an electric field onto the first
of a series of dynodes. As the electrons collide with the first dynode, secondary electrons
are emitted via the Auger effect and are in turn directed to the second dynode and the
third, each time multiplying in number until reaching the anode where they are read out
by charge sensitive electronics. The “gain” of a PMT is the average total amplification of
the entire dynode chain, and can range anywhere from ∼105 to ∼108 [81].
139
In order to calibrate the PMT gain, a spectrum is obtained from single photoelectrons
(SPE), which is then fit with a function to model the output distribution. The gain is
then determined from the best fit parameters. Exactly which function provides the best
representation of the PMT output is not clear, although many approaches have been
made in the literature [118, 119]. The reason for the non-consensus is that determination
of an explicit expression for the PMT output probability distribution appears to be
intractable [120]. This chapter approaches the problem from an analytic perspective,
followed by a quantitative test of several approximations to the output probability
distribution, and finally an evaluation of an independent gain determination method.
7.1 Analytic Approach to the Single Photoelectron Spectrum
The emission of secondary electrons at each dynode is typically understood as
being a Poisson process [119]. That is, the number of electrons, t, leaving each dynode
is a random number following a Poisson distribution with mean equal to the number of
incident electrons multiplied by the amplification factor of the dynode, Pnλ(t), where λ
is the dynode’s amplification factor (typically around 3 to 5 [81]) and n is the number of
incident electrons. Although some attention has been focused on departures of secondary
emission from Poissonianity, there is no clear evidence for this [121]. I label the probability
of receiving t electrons from the N th dynode as PN(t). Because I am considering the
behavior of the SPE spectrum, the number of electrons incident upon the first dynode is
unity, and therefore the probability of obtaining t electrons from the first dynode, P1(t),
is given simply by a Poisson distribution with mean of λ,
P1(t) = Pλ(t) =λte−λ
t!. (7–1)
Understanding the probability distribution of electrons from the second dynode is
more complicated, because any possible output from the first dynode must be considered.
For example, the probability of obtaining a single electron from the second dynode is given
140
by,
P2(1) = Pλ(1)Pλ(1) + Pλ(2)P2λ(1) + Pλ(3)P3λ(1) + · · · , (7–2)
where the first Poisson in each term represents the probability of obtaining a certain
number of electrons from the first dynode, and the second Poisson is the probability of
getting only one electron from the second dynode. This can be generalized any number of
final electrons, t, as,
P2(t) =∞∑
n=0
Pλ(n)Pnλ(t). (7–3)
As the number of dynodes under consideration increases, the mathematical expression
for the final probability distribution becomes more complicated. However, the statistical
structure remains the same: the spectrum of electrons from the N th dynode is still a
Poisson distribution convolved with the spectrum from the (N − 1)th dynode, written as,
PN(t) =∞∑
n=0
PN−1(n)Pnλ(t). (7–4)
This recursive relation can be traced backwards from the N th dynode all the way to the
first dynode,
PN(t) =∞∑
k=0
∞∑
l=0
· · ·∞∑
m=0
∞∑n=0
Pλ(n)Pnλ(m) · · ·Plλ(k)Pkλ(t), (7–5)
or, written more compactly,
PN(nN) =N−1∏m=0
∞∑nm=0
Pnmλ(nm+1)δn0,1, (7–6)
where t from the previous relations has been replaced with nN . The Kronecker delta
is used because the first dynode always receives exactly one electron. Here, it has been
assumed that each dynode contributes exactly the same amplification factor, λ. However,
generalizing to non-uniform dynode amplification can be done simply by replacing λ with
a set, λm. Figure 7-2 shows the result of Equation 7–6 with λ = 4 and N = 1, 2, 3, 4. The
resolution of each distribution, shown as σ/µ where σ2 is the variance and µ is the mean,
141
nN+1
Pro
babi
lity
N=1 N=2
N=3
N=4
σ/µ=0.500
σ/µ=0.573
σ/µ=0.576
σ/µ=0.559
100
101
102
103
10−4
10−3
10−2
10−1
Figure 7-2. Analytic probability distribution of a photomultiplier tube output after Ndynodes (Equation 7–6), each with an amplification factor of 4. The verticaldashed lines are located at (4N + 1), where 4N is the mean of eachdistribution. The horizontal axis is given as nN + 1 so that nN = 0 can beshown on this log-log plot.
increases at each step. However, the amount of increase diminishes; this is reflective of
the fact that the resolution of the final signal is expected to be roughly proportional to a
geometric series in λ−1 [81],
σ
µ∝ 1
λ+
1
λ2+ · · ·+ 1
λN∼= 1
λ− 1. (7–7)
and that the overall signal resolution is dominated by the level of fluctuations at the first
few dynodes. It is for this reason that PMTs are often designed so that the amplification
of the first dynode is larger than any of the other dynodes. The spike in probability at
nN = 0 is caused mainly by photoelectrons that die at the first dynode, and is called the
“impulse density” by Stokey and Lee [119]. Because an output of nN = 0 at any dynode is
equivalent to no signal at all, the impulse density is typically ignored.
Though Equation 7–6 is compact, it is not at all useful. A typical PMT has no fewer
than ten dynodes, in which case using Equation 7–6 to calculate even a single value of nN
becomes computationally prohibitive. Additionally, even at N = 3 it is clear that typical
142
values of nN are large enough that the discrete nature of Equation 7–6 can be adequately
approximated as being continuous.
7.2 PMT Monte Carlo and Function Test
The typical SPE spectra from the PMTs used in the Xurich were shown in Section
5.3. Two spectra, one from each PMT, are shown again here in Figure 7-3. In orderC
ount
s
ZB2183
0 5 10 15
x 106
100
101
102
103
104
105
nN
TC1978
0 5 10 15 20
x 106
Figure 7-3. An example of real PMT single photoelectron spectra, also shown in Figure5-7.
to obtain such a spectrum, the PMT is illuminated by a pulsed, blue light emitting
diode (LED), with a pulse duration of 4 µs and a repetition rate of 1 kHz. Within each
pulse, the central 1 µs is integrated. The intensity of the LED is adjusted so that roughly
95% of the LED pulses give no PMT signal. With this small probability of success, the
number of photoelectrons falling within the 1 µs signal window is Poisson distributed
with an average of − ln(0.95) = 0.0513 photoelectrons. Such a low intensity is chosen
in order to minimize the contribution from double and triple photoelectrons. With this
average number, the frequency of double photoelectrons relative to single photoelectrons
is − ln(0.95)/2 = 0.026, and hence the resulting spectrum has a negligible contamination
from multiple photoelectron emission.
The large peak near zero, called the pedestal, is due to the integration of baseline
noise and is treated as being Gaussian distributed; here it is clear why the impulse density
143
is neglected. Another reason that Equation 7–6 is not useful is that a real PMT spectrum
will have instrumental noise fluctuations applied in addition to the true fluctuations
already resulting from the amplification process. A fit to the spectrum of Figure 7-3
can be made with several different functions [118, 119], and three are investigated here:
Gaussian, truncated Gaussian, and continuous Poisson.
For some PMTs, the peak value of the SPE response is significantly separated from
the pedestal that the SPE spectrum can be approximated by a three parameter Gaussian
function:
G(H, µ, σ; x) = He−(x−µ)2/σ2
(Gaussian function). (7–8)
If the peak of the SPE response is non-negligibly close to the pedestal, as in Figure
7-3, the non-physical negative portion of the Gaussian function must suppressed, or
‘truncated’. The result has the same parameterization as the Gaussian function, but is
defined to be zero for negative values of x:
T (H, µ, σ; x) = θ(x)He−(x−µ)2/σ2
(Truncated Gaussian), (7–9)
where θ(x) is the Heaviside step function. Although the parameterizations of the Gaussian
and truncated Gaussian are the same, the extracted gain value, given as the mean of the
distribution (not µ), will be different due to the differing range over which the function
is non-zero. Additionally, the fit itself will return different values of the three parameters
because negative vales of the output signal will skew the Gaussian fit.
A third function is motivated by the fact that the shape of the SPE distribution is
determined mainly by the output of the first few dynodes, which give a (discrete) Poisson
spectrum of secondary electrons. The Poisson distribution, Equation 7–1, is converted to
a continuous function by the introduction of a normalization parameter, A, a continuous
independent variable, t → x, a gamma function, k! → Γ(x + 1), and a scale parameter, B:
C(A,B, λ; x) = θ(x)Aλx/B
Γ( xB
+ 1)(Continuous Poisson). (7–10)
144
The factor e−λ does not affect the spectral shape and has been absorbed into A. The
mean and variance of this distribution cannot be found by an analytic combination of the
fit parameters, and must instead be determined by numerical integration.
In order to test the performance of these three fitting functions, a Monte Carlo
is constructed to simulate the PMT output. The simulation employs six different
configurations of dynode amplification factors, shown in Table 7-1, chosen to produce
SPE spectra that are characteristically similar to those seen in Figure 7-3. The results
from one simulation are shown in Figure 7-4.
Config: 1
0 2 4 6 8 10
x 106
100
101
102
103
104
Config: 2
0 2 4 6 8 10
x 106
100
101
102
103
104
Config: 3
0 2 4 6 8 10
x 106
100
101
102
103
104
nN
Cou
nts
Config: 4
0 2 4 6 8 10
x 106
100
101
102
103
104
Config: 5
0 2 4 6 8 10
x 106
100
101
102
103
104
Config: 6
0 2 4 6 8 10
x 106
100
101
102
103
104
Figure 7-4. An example of one of the 1000 sets of simulated spectra generated by theMonte Carlo simulation. Colors represent the pedestal (blue), singlephotoelectrons (red), double photoelectrons (green), sum (black), and the truegain (cyan).
Each simulation begins by picking a random number from a binomial distribution
with 105 trials and 95% probability of success; this number, Np, represents the number of
events in the pedestal. The number of single, Ns, and double, Nd, photoelectron events
are similarly chosen. These single and double events are used as input to the dynode
simulation, which takes the input number of photoelectrons as incident on the first
dynode, and choses a number from a Poisson distribution with mean of λ multiplied by
the input number. This resulting number is then treated as input to the second dynode,
145
Table 7-1. The dynode amplification factors used in the six configurations simulated bythe Monte Carlo. An arrow indicates that the same value is used in allsubsequent dynodes. The bar charts on the right show the performance of theGaussian (purple), truncated Gaussian (blue), and continuous Poisson (green)fitting functions. Performance is quantified by the relative bias, b/µt where b isthe estimator bias of the gain and µt is the true gain, and the relative standarddeviation, σ/µt where σ is the estimator standard deviation. These values aredetermined from the histograms in Figure 7-5. By both measures, thetruncated Gaussian consistently outperforms the other two functions.
Config Dyn1 Dyn2 Dyn3 Dyn4 Dyn5-12b/µt σ/µt
−0.1 0 0.1 0 0.02 0.04
1 3.4 −→
2 3.3 −→
3 3.2 −→
4 3.1 −→
5 3.0 −→
6 2.0 2.5 3.0 3.0 3.7 −→
and repeated until passing through all twelve dynodes. This process is repeated for each
Ns and Nd. The three spectra (pedestal, single p.e., and double p.e.) are then convolved
with a Gaussian to simulate baseline noise. The sum of these spectra are fit with a
Gaussian (for the pedestal) plus each of the three fit functions individually.
This process is carried out 1000 times, each time the gain estimators are saved; the
spectra of gain estimators from the three fit functions are shown in Figure 7-5 for each
of the six dynode configurations. These spectra are then used to determine the estimator
bias and estimator variance.
Upon visual inspection of Figure 7-5, the truncated Gaussian and continuous Poisson
functions appear to have equivalent estimator variance, while the truncated Gaussian
shows consistently smaller estimator bias. The actual bias and variance are shown in Table
7-1, and bear out this qualitative assessment.
146
Config: 1
1.8 2 2.2 2.4 2.6
x 106
100
101
102
103
Config: 2
1.3 1.4 1.5 1.6 1.7 1.8
x 106
100
101
102
103
Config: 3
0.8 0.9 1 1.1 1.2 1.3
x 106
100
101
102
103
Gain Estimator
Cou
nts
Config: 4
5 6 7 8 9
x 105
100
101
102
103
Config: 5
4 4.5 5 5.5 6 6.5
x 105
100
101
102
103
Config: 6
1.2 1.4 1.6 1.8 2
x 106
100
101
102
103
Figure 7-5. Distributions of the gain estimators of the three SPE fit functions described inthe text. Colors represent Gaussian (purple), truncated Gaussian (blue), andcontinuous Poisson (green). In each frame, the vertical black line representsthe true gain.
7.3 The Indirect Gain Estimation Method
The gain estimation methods outlined in previous section constitute direct gain
measurements. That is, they seek to track a known number of input electrons and measure
the output. There exists in the LXe literature an indirect method used by Baldini et
al. [122]. Incidentally, the PMTs used in [122] (Hamamatsu R6041Q) are very similar to
those used in the Xurich detector.
Instead of a low-intensity LED intended to produce single photoelectrons, Baldini et
al. use a LED of varying intensities and take advantage of the fact that the fluctuations
in the number of photoelectrons is coupled to their absolute number. From counting
statistics, the relation between the signal variance, the gain, and the charge output, is,
σ2 = ge(q − q0) + σ20, (7–11)
where g is the multiplier gain, e is the electron charge, σ2 is the variance, q is the charge
at the PMT output, and the ‘0’ subscript indicates those values of the pedestal (integrated
147
baseline). From a set of measurements with varying LED illumination, a plot is made of
σ2 versus q from which a slope is extracted and equated to ge.
Though straightforward, this method considers only fluctuations in the photoelectron
emission, while completely neglecting fluctuations in the photoelectron amplification. That
is, it treats the SPE response as having zero variance. Including the SPE variance results
in,
σ2 = ge(1 + r2)(q − q0) + σ20, (7–12)
where r is the resolution of the SPE spectrum (in terms of σ/µ). If the SPE resolution is
negligible (i.e. r ¿ 1), then (1 + r2) ≈ 1 and Equation 7–12 reduces to Equation 7–11.
However, the SPE spectra of Figure 7-3 have r-values of ∼0.8 (left) and ∼0.6 (right),
and therefore use of this method to determine g would result in an error of 64% and 36%,
respectively. The plot of σ2 versus q is still linear, but measurement of its slope offers no
way to separately determine g and r.
Charge from anode [nC]
Cou
nts
0 0.05 0.1 0.15 0.2 0.25 0.310
1
102
103
104
Figure 7-6. Spectra of PMT output from varying the LED intensity.
However, this technique can provide a check of the parameters obtained in the SPE
fit. Figure 7-6 shows the spectra from ZB2183 illuminated at several different intensities.
The mean versus variance of these peaks are shown in Figure 7-7. The red line is a fit to
all five data points. This line has a slope that is roughly 35% higher than what is expected
from the SPE spectrum of this same PMT. It is possible that the PMT suffers from
nonlinearity at the highest illuminations; indeed, if this is the case then the variance would
148
Qanode
[C]
σ anod
e2
[C2 ]
0 0.5 1 1.5 2 2.5 3
x 10−10
0
0.5
1
1.5
2
2.5
3
3.5x 10
−22
Qanode
[C]
σ anod
e2
[C2 ]
0 1 2 3
x 10−11
0
1
2
3x 10
−23
Slope = 1.1486e−12Slope = 8.6529e−13
eg(1+r2) = 8.4699e−13
Figure 7-7. Variance versus mean for PMT output in response to various LEDilluminations. The insert axes are a zoom of the three lowest data points,which were used for the green-line fit.
be unchanged, while the mean would be lower than expected, giving a higher slope than
that predicted from low-illumination measurements. When, instead, only the three lowest
data points are used in the fit (green line), the slope is within 2% of the value derived
from the SPE spectrum.
149
CHAPTER 8CONCLUDING REMARKS
The more we learn about the world, and the deeper our learning, the more conscious,specific, and articulate will be our knowledge of what we do not know, our knowledge ofour ignorance. For this, indeed, is the main source of our ignorance—the fact that our
knowledge can only be finite, while our ignorance must necessarily be infinite.
-Karl Popper
The XENON10 results of Chapter 3 represent an important result from several
different perspectives. First, at the time of its release, the results for SI interactions
represented the most sensitive search ever, and indeed remains the most sensitive
measurement for WIMP masses below 40–50GeV c−2 (Figure 3-23). XENON10’s
exclusion limits on the pure-neutron SD cross section are the most sensitive for all WIMP
masses. Second, XENON10 achieved these sensitivities in the first results. XENON10 was
constructed as a proof of principle detector, and in its first run was able to surpass the
best results of other searches using technologies far more mature. If LXe can yield such
impressive results in its proof of principle application, then future searches using larger,
more sophisticated LXe detectors are sure to dominate the field.
While not yet sensitive to the values of the SI WIMP-nucleon cross section most
favored by the neutralino, XENON10 has been able to exclude a significant portion of the
parameter space deemed to lie within the 95% probability contour for for SUSY models.
SD sensitivity to relevant neutralino interactions remains weak, however, this study has
managed to exclude for the first time heavy Majorana neutrinos with masses favored by
particle theories. In combination with results from LEP, the limit on the mass of the
heavy Majorana neutrino is excluded below 2.2TeV c−2.
The XENON10 experiment has also pushed the limits of energy threshold lower than
other LXe detectors. In doing so, an energy range in which Leff was poorly understood
suddenly became important in understanding XENON10’s sensitivity. The uncertainty
in XENON10’s results coming from the lack of Leff understanding was discussed at the
beginning of Chapter 4, and presented a strong motivation for further study of this
150
quantity. This chapter presented a measurement of precisely this; with the Xecube
detector, Leff was measured for nuclear recoils as low as 5 keV. The previously assumed
flat Leff = 0.19 behavior was shown to be inconsistent with these beam measurements
at energies below 10 keV. Instead, it appears that Leff drops from ∼0.2 at energies above
20 keV to ∼0.14 at 10 keV and below.
Given the promising future in store for LXe dark matter detectors, new techniques
must be developed for energy calibration. The traditional techniques are not very useful
in the context of dark matter searches. Chapter 6 presented a new technique for LXe
energy calibration: 83mKr. Use of this source is non-trivial, but was demonstrated with
remarkable success in the Xurich detector, whose development was presented in Chapter
5. 83mKr was not only shown to have the advantage of offering a background-free method
of measurement at low energies, the method of introduction into the detector was shown
to be free of any radioactive contaminants capable of hindering a low-background WIMP
search.
The Xurich detector not only facilitated a successful implementation of this new
calibration source, but was used to study some properties of LXe at these low energies,
relevant for dark matter searches. The light yield, at zero applied field, was observed to
show nonlinearities at the level of ∼6% between 122 keV and 9.4 keV.
Liquid xenon is expected to play an important role in the future of dark matter direct
detection, and could very well be the first technology to probe the regions of parameter
space most interesting for SUSY, at the same time that SUSY is being probed with
proton-proton collisions at the LHC. The studies presented in this dissertation provide
important developments in the understanding of LXe in the context of dark matter
searches, in addition to the development of techniques that will prove useful for future
experiments.
151
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BIOGRAPHICAL SKETCH
Aaron Gosta Manalaysay was born in Bethesda, Maryland, spending most of his
youth in the Washington D.C. area. In grade school he began playing the saxophone, later
becoming involved in various funk, rock, and jazz bands. His music activities, always a
competition for his time with academics, finally came to an end when he started graduate
school.
Aaron enrolled at Case Western Reserve University (CWRU), in Cleveland, Ohio.
Following a set of positive experiences in his freshman physics courses, he decided to
major in physics and stay in the field as long as it held his interest. In his junior year
at CWRU he saw a talk given by Professor Dan Akerib on the field of dark matter
direct detection. Immediately following the talk, he approached Dan and asked to do
his bachelor’s thesis in that group. His bachelor’s thesis, entitled Simulating the neutron
background in the CDMS-II experiment, focused on the prospect of using proportional
counter gas tubes in order to veto fast neutrons resulting from hadronic cascades induced
by cosmic-ray muons traveling through the rock surrounding the Soudan mine where the
CDMS-II experiment was located.
Following graduation, Aaron worked for a year in Akerib’s CDMS group, working
as a lab technician. During this time, he decided to go to the University of Florida (UF)
for graduate school, and later met Laura Baudis (then a post-doc in CDMS, and later,
coincidentally, taking a faculty position at UF) and learned about the then proposed
XENON dark matter search. While in his first year as a graduate student at UF, Aaron
decided to approach Laura about doing his dissertation in her group. This choice led him
to eventually leave Florida after his third year and travel to Italy, Germany, New York,
and finally Switzerland, where he finished his dissertation.
In the rare moments that he has free time, Aaron enjoys rock climbing, hiking,
mountain biking and snowboarding. He plans to stay in Zurich following his Ph.D. while
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working jointly on research and development (R&D) for tonne-scale liquid noble dark
matter detectors, and on R&D for the next generation of Cherenkov telescopes.
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