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BOSTONUNIVERSITY
Robert CareyMuLan CollaborationBoston University
The MuLan ExperimentA New Measurement of the Fermi Constant
Berkeley, Boston University, University of Illinois, James Madison, University of Kentucky, KVI, PSI
Outline:●Motivate the measurement●Describe the experiment●Final results
Precision electroweak predictions rest on three parameters
Fermi Constant
Giovanetti et al1984
±GF
GF¼ 9 ppm
Mass of the neutral weak boson
LEP EWWG2005
±MZ0
MZ0¼ 23 ppm
Fine Structure Constant
Gabrielse et al 2008
±®em
®em¼ 0:37ppb0.37 ppb
RMC, PANIC, July 2011
The V-A theory factorizes into a pure weak contribution, and non-weak corrections, essentially uncontaminated by hadronic uncertainties.
Muon decay gives us unique access to the electroweak scale
The muon only decays via the weak interaction, which gives it a very long lifetime.
All relevant weak interaction physics confined to one easily(!) measured parameter with a clean theoretical interpretation.
RMC, PANIC, July 2011
The Fermi constant is an implicit input to all precision electroweak studies
Contains all weak interaction loop corrections.
RMC, PANIC, July 2011
The Fermi constant is an implicit input to all precision electroweak studies
Plot clipped from LEP Electroweak Working Group publications
Contains all weak interaction loop corrections.
Top quark mass prediction:
+
e
W t
b
W e
+
+
+
RMC, PANIC, July 2011
±GF
GF=
1
2
sµ±¿¹
¿¹
¶2+
µ5±m¹
m¹
¶2+
µ±theory
theory
¶2
18 ppm 90 ppb 30 ppmMid 90s: 17 ppm 90 ppb
Standard Model Fermi Constant extraction used to be theory-limited
T. van Ritbergen and R. G. Stuart, Nucl. Phys. B564, 343 (2000)
RMC, PANIC, July 2011
±GF
GF=
1
2
sµ±¿¹
¿¹
¶2+
µ5±m¹
m¹
¶2+
µ±theory
theory
¶2
van Ritbergen and Stuart: 2-loop QED corrections (massless electrons)
18 ppm 90 ppb < 0.3 ppm1999: 9 ppm 90 ppb
Lifetime error now limits the Fermi constant
Standard Model Fermi Constant extraction used to be theory-limited
T. van Ritbergen and R. G. Stuart, Nucl. Phys. B564, 343 (2000)
RMC, PANIC, July 2011
±GF
GF=
1
2
sµ±¿¹
¿¹
¶2+
µ5±m¹
m¹
¶2+
µ±theory
theory
¶2
1 ppm < 0.3 ppmGoal: 0.5 ppmLifetime error now limits the Fermi constant
Standard Model Fermi Constant extraction used to be theory-limited
T. van Ritbergen and R. G. Stuart, Nucl. Phys. B564, 343 (2000)
RMC, PANIC, July 2011
Also ....Two muon capture experiments at PSI
Protium: MuCapDeuterium: MuSun...(where the capture rate is inferred from the difference between the positive and negative muon lifetimes) require measurements of thepositive muon lifetime to 10 ppm or better.
For 1ppm, need more than 2 trillion muons ...
πE3 Beamline, Paul Scherrer Institut, Villigen, Switzerland
For 1ppm, need more than 2 trillion muons ...
πE3 Beamline, Paul Scherrer Institut, Villigen, Switzerland
For 1ppm, need more than 2 trillion muons ...
πE3 Beamline, Paul Scherrer Institut, Villigen, Switzerland
+12.5 kV
-12.5 kV
… with a pulsed time structure
SlitTarget Kicker
Mu
ons
in t
arg
et
+12.5 kV
-12.5 kV
… with a pulsed time structure
SlitTarget Kicker
Mu
ons
in t
arg
et
5¹s
On
Nin(t) = R¹¿³1¡ e¡t=¿
´
+12.5 kV
-12.5 kV
… with a pulsed time structure
SlitTarget Kicker
Mu
ons
in t
arg
et
22¹s5¹s
On Off
Nin(t) = R¹¿³1¡ e¡t=¿
´
Nout(t) = Nin(tc)e¡t=¿
+12.5 kV
-12.5 kV
… with a pulsed time structure
SlitTarget Kicker
Mu
ons
in t
arg
et
22¹s5¹s
On Off
Nin(t) = R¹¿³1¡ e¡t=¿
´
Nout(t) = Nin(tc)e¡t=¿
Modulators designed, built at TRIUMF
Plates, vacuum chamber built by PSI
RMC, PANIC, July 2011
Symmetric, highlysegmented detector
Thinstopping
target
We have reached our goal by running about 20 muon decay experiments simultaneously
Polarized surfacemuon beam
RMC, PANIC, July 2011
Symmetric, highlysegmented detector
Thinstopping
target
We have reached our goal by running about 20 muon decay experiments simultaneously
+12.5 kV
-12.5 kV
Polarized surfacemuon beam
Electrostaticbeam kicker
RMC, PANIC, July 2011
Symmetric, highlysegmented detector
Thinstopping
target
We have reached our goal by running about 20 muon decay experiments simultaneously
+12.5 kV
-12.5 kV
Polarized surfacemuon beam
Electrostaticbeam kicker
Inner/Outertile pair
RMC, PANIC, July 2011
Symmetric, highlysegmented detector
Thinstopping
target
We have reached our goal by running about 20 muon decay experiments simultaneously
+12.5 kV
-12.5 kV
Polarized surfacemuon beam
Electrostaticbeam kicker
Inner/Outertile pair
500 Mhzwaveformdigitization
MHTDC(2004)
RMC, PANIC, July 2011
Symmetric, highlysegmented detector
Thinstopping
target
We have reached our goal by running about 20 muon decay experiments simultaneously
+12.5 kV
-12.5 kV
Polarized surfacemuon beam
Electrostaticbeam kicker
Inner/Outertile pair
500 Mhzwaveformdigitization
N(t) = N0e¡t=¿ +B
MHTDC(2004)
RMC, PANIC, July 2011
Data Production in 2006-7
2006: 1.16 ppm (stat.)2007: 1.7 ppm (stat.)
We collected roughly a trillion muons each year
23
Time-dependent systematic errors are the principal analysis issue
Early-to-late changes:
Time in fill
log(
coun
ts)
24
Time-dependent systematic errors are the principal analysis issue
Early-to-late changes:
Instrumental issuesPMT time pickoff, gainPulse shape variationsKicker voltage sag and beam dynamics effectsPileup : does detector
system performance change when pulses get
close together?
Time in fill
log(
coun
ts)
25
Time-dependent systematic errors are the principal analysis issue
Early-to-late changes:
Instrumental issuesPMT time pickoff, gainPulse shape variationsKicker voltage sag and beam dynamics effectsPileup : does detector
system performance change when pulses get
close together?Physics issues
Spin (de)polarizationand precessionNon-flat background
Time in fill
log(
coun
ts)
26
Time-dependent systematic errors are the principal analysis issue
Ee
threshold
time
coun
tsi
Early-to-late changes:
Instrumental issuesPMT time pickoff, gainPulse shape variationsKicker voltage sag and beam dynamics effectsPileup : does detector
system performance change when pulses get
close together?Physics issues
Spin (de)polarizationand precessionNon-flat background
Time in fill
log(
coun
ts)
1 cut data selection
Pileup
time
A MuLan Detector
Tile
Hidden pulses distort lifetime ~ 100 ppm, if uncorrected
PulseResolving
Time
Pileup
time
A MuLan Detector
Tile
Hidden pulses distort lifetime ~ 100 ppm, if uncorrected
time
coun
ts
Ppileup /
Z tr
0
P (t)P (t+ t0)dt0
/ e¡2t=¿
PulseResolving
Time
Pileup goes as Rate2
Don't fit for pileup losses(big statistical cost) => reconstruct!
A MuLan Detector
Tile
Don't fit for pileup losses(big statistical cost) => reconstruct!
A MuLan Detector
TileArtificial
ResolvingTime
time
Fill n
ArtificialResolving
Time
Fill n+1
Don't fit for pileup losses(big statistical cost) => reconstruct!
Pileup Time Distribution
Normal Time Distribution
A MuLan Detector
TileArtificial
ResolvingTime
time
Fill n
ArtificialResolving
Time
Fill n+1
Adding the pileup distribution to the normal distribution corrects for what's missing ...- and is more robust than simple extrapolation to ADT = 0
Don't fit for pileup losses(big statistical cost) => reconstruct!
Pileup Time Distribution
Normal Time Distribution
A MuLan Detector
TileArtificial
ResolvingTime
time
Fill n
ArtificialResolving
Time
Fill n+1
Adding the pileup distribution to the normal distribution corrects for what's missing ...- and is more robust than simple extrapolation to ADT = 0
How well does our method correct the pileup?
1 p
pm
There is a small (1 ppm) unexplained change in the lifetime (R) with artificial dead time
- as if 0.1 % is unaccounted for
RMC, PANIC, July 2011
Muon spins precess in magnetic fields:The component parallel to B is static...
... while the perpendicular component precesses.
RMC, PANIC, July 2011
Muon spins precess in magnetic fields:The component parallel to B is static...
... while the perpendicular component precesses.
Residual polarization of muon ensemble decays over measurement period ...
… with different lifetimes for the perpendicular (transverse) and parallel(longitudinal) components.
RMC, PANIC, July 2011
Muon spins precess in magnetic fields:The component parallel to B is static...
... while the perpendicular component precesses.
Residual polarization of muon ensemble decays over measurement period ...
… with different lifetimes for the perpendicular (transverse) and parallel(longitudinal) components.
And decay positrons are emitted preferentiallyalong spin
RMC, PANIC, July 2011
You can fit for the precession and depolarization… but it aint easy
ND(t) = N0e¡t=¿
µ1 +
1
3
h~Pk(0) ¢ eDe
¡t=Tk + ~P?(t) ¢ eDe¡t=T?i¶
RMC, PANIC, July 2011
You can fit for the precession and depolarization… but it aint easy
ND(t) = N0e¡t=¿
µ1 +
1
3
h~Pk(0) ¢ eDe
¡t=Tk + ~P?(t) ¢ eDe¡t=T?i¶
Exponential lifetime decay ...
... of a system with non-zero initial ensemble polarization ...
RMC, PANIC, July 2011
You can fit for the precession and depolarization… but it aint easy
ND(t) = N0e¡t=¿
µ1 +
1
3
h~Pk(0) ¢ eDe
¡t=Tk + ~P?(t) ¢ eDe¡t=T?i¶
Exponential lifetime decay ...
... precessing in time ...
... of a system with non-zero initial ensemble polarization ...
... with orientation and material dependent lifetimes.
RMC, PANIC, July 2011
We start with nearly 100% polarized beam ... how do we control polarization effects?
RMC, PANIC, July 2011
We start with nearly 100% polarized beam ... how do we control polarization effects?
Detector A
Detector A'
(µ; Á)
(¼ ¡ µ; ¼ + Á)
Central Target
Apart from acceptance differences, point symmetry of the detector cancels polarization asymmetries in the sum over symmetric tile pairs
RMC, PANIC, July 2011
We start with nearly 100% polarized beam ... how do we control polarization effects?
Detector A
Detector A'
(µ; Á)
(¼ ¡ µ; ¼ + Á)
Central Target
Apart from acceptance differences, point symmetry of the detector cancels polarization asymmetries in the sum over symmetric tile pairs
Uniform 3-pi coverage!
RMC, PANIC, July 2011
We also minimize the remnant polarization itself, by choice of target environment
A polarization destroying ferromagnetic target, AK3, with high internal field (2004,2006)
RMC, PANIC, July 2011
We also minimize the remnant polarization itself, by choice of target environment
A polarization destroying ferromagnetic target, AK3, with high internal field (2004,2006) Or dephasing alone...
Polarization preserving and muonium forming target, crystalline quartz, with an applied external field (2007)
RMC, PANIC, July 2011
We also minimize the remnant polarization itself, by choice of target environment
A polarization destroying ferromagnetic target, AK3, with high internal field (2004,2006) Or dephasing alone...
Polarization preserving and muonium forming target, crystalline quartz, with an applied external field (2007)
We also minimize muon stops outside the controlled target region with a vacuum beam corridor directly to the target (2006, 2007)
RMC, PANIC, July 2011
In 2006 data, spin polarization was not an issue...
RMC, PANIC, July 2011
In 2006 data, spin polarization was not an issue...
… but in 2007 data, it was.
RMC, PANIC, July 2011
Dozens of systematic runs taken in 2007 are consistent
Can sum all detectors and fit or fit individualdetectors and then average : same result
In 2006 data, spin polarization was not an issue...
… but in 2007 data, it was.
RMC, PANIC, July 2011
Blindanalysis
Final 2006-7 Error Table
RMC, PANIC, July 2011
0.3 ppm difference!
Blindanalysis
Final 2006-7 Error Table
RMC, PANIC, July 2011
11ppm 16ppm
The old world average was driven by two recent measurements
FAST Collaboration, Phys.Lett.B663:172-180,2008
RMC, PANIC, July 2011
Final results: D.M. Webber et al., Physical Review Letters 106, 041803 (Jan. 2011)PRD in progress
RMC, PANIC, July 2011
Conclusions
1. Using two very different techniques, we have made two consistent measurements of themuon lifetime and thus of the Fermi constant.
RMC, PANIC, July 2011
Conclusions
1. Using two very different techniques, we have made two consistent measurements of themuon lifetime and thus of the Fermi constant.
2. Both measurements are consistent with our 2004 result and those of other groups.
RMC, PANIC, July 2011
Conclusions
1. Using two very different techniques, we have made two consistent measurements of themuon lifetime and thus of the Fermi constant.
2. Both measurements are consistent with our 2004 result and those of other groups.
3. Statistical errors are slightly larger thansystematic errors, which are, in turn, slightly largerthan current theoretical uncertainties.
RMC, PANIC, July 2011
Conclusions
1. Using two very different techniques, we have made two consistent measurements of themuon lifetime and thus of the Fermi constant.
2. Both measurements are consistent with our 2004 result and those of other groups.
3. Statistical errors are slightly larger thansystematic errors, which are, in turn, slightly largerthan current theoretical uncertainties.
Muon lifetime: 2196981.3 +/- 2.3 ps
RMC, PANIC, July 2011
(Most of)The MuLan Collaboration
RMC, PANIC, July 2011
Backup Slides
RMC, PANIC, July 2011
Where's the bucket?
There's the bucket!
MuLan: “The world's largest research-grade soccer ball”
RMC, PANIC, July 2011
Result is consistent across analysis conditions
RMC, PANIC, July 2011
Consistency over data set: 2006
RMC, PANIC, July 2011
Residual polarization (along z) is a is a very small effect
upstream downstream
Slope in R: 13 ppm/detector half
RMC, PANIC, July 2011
Our analyzers do not know the size of a clock tick
And neither do the rest of us!
Time in clock ticks
Counts
RMC, PANIC, July 2011
It doesn't matter when you start the fit
RMC, PANIC, July 2011
RMC, PANIC, July 2011
Treating each detector as a separate experiment
Many-at-onceNeed time structured (AC) beam, not a continuous (DC) beam
Electron timeline
Muon timeline
Wrong assignments
Right assignmentsMuch higher rates, but much harder experiment R&D and construction
BeamOff
BeamOff
BeamOn
BeamOn
time
coun
ts
One-at-a-time
Can't really do one-at-a-time, the next best thing is a low rate, DC beam.
Muon timeline
Electron timeline
time
coun
ts
Wrong assignments
Right assignments S
B/N
N2=
1
N
30 kHz! 385 d for 1012¹+
RMC, PANIC, July 2011
The muon lifetime is similarly crucial for nucleon weak structure functions
V® = gV (q2)°® +
igM(q2)
2MN
¾®¯q¯
A® = gA(q2)°®°5 +
gP (q2)
m¹
q®°5
iM =GFVudp
2hºj °®(1 ¡ °5) j¹i hnj V® ¡ A® jpi
gV ; gM ; gA Well known from other experiments
¤S
RMC, PANIC, July 2011
The muon capture rate is determined by a lifetime difference technique
! ¤S =1
¿¹¡¡
1
¿¹+
log
(co
un
ts)
time
μ+μ –
¢¿ ¼ 0:146%±gP
gP¼ 5
±¤S
¤S
5% 1%
±¿¡¿¡
! 10¡5
¤¹¡ = ¤¹free +¤S
Andreev, et.al. Phys. Rev. Lett. 99, 032002 (2007)
RMC, PANIC, July 2011
A brief history...
Before 2007, the best measurements were over 20 years old, and until 1999, G
F
was theory limited.
G. Bardin et al., Phys. Lett. B 137, 135 (1984)K. Giovanetti et al., Phys. Rev. D 29, 343 (1984)
RMC, PANIC, July 2011
QED Theory Uncertainties
● Hadronic uncertainties give 10–8 ● Dominant errors come from uncalculated
effects:● Three loop estimates give 1.4 × 10–7 ● Two loop logs give 1.7 × 10–7
● Overall, theory errors are a “few 10–7”
RMC, PANIC, July 2011
Definitions: PDG vs vRS
Conventional, but really a weak interaction correction. Van Ritbergen and Stuart leave this out as inconsistent with principle, while Erler and Langacker leave it in (PDG review)
Massive part of the phase space integration
1-loop QED corrections
RMC, PANIC, July 2011
Standard Electroweak Model
● All 1-loop corrections known (Sirlin)● Most (all?) two loop corrections known● Important class of contributions related to
oblique corrections (vector boson self-energies)
RMC, PANIC, July 2011
The Fermi constant beyond the Standard Model
Non-zeroneutrino mass
Non-standardMichel parameters
Heavy weakgauge bosons
< 3 ppm
< 70 ppm
RMC, PANIC, July 2011
Extra Slides
Watching the bucket empty
This gives about 40 MB/s of data that has to be stored!
The PMTs feed the WFDs
RMC, PANIC, July 2011
We have made much progress in proving that our results are consistent across various conditions
Fit start time scans show no evidence of missing long time scale components
The lifetimes measured by individual detector pairs are statistically consistent
FAST @ PSI: 2 ppm goal■ Basic idea: Take many events “at once” using an imaging
detector ■ Locate stops, π + → µ + decays, and µ + → e+ decays
and track them■ Advantage: No beam structure to worry about
π +
First result reported in July 2007: δτ µ = 16 ppm
RMC, PANIC, July 2011
MuCap Experiment
Stop µ - in 10 atm pure hydrogen … and image stop location
ΛTΛS
µ
ppµ
ppµ
pµpµ
Λortho
Λpara
F=0 F=1
J=1
J=0
λOP
λOP (ms-1)
gP
20 40 60 80 100 120
2.5
5
7.5
10
12.5
15
17.5
20
µ - + p → νµ + n + γ @ TRIUMF
Saclay exp theory TRIUMF 2005
µ- + p →
νµ + n @ Saclay ChP
T
Previous experiments cannot be interpreted due to muon molecular chemistry ambiguities
TPC stopping volume