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University of Nebraska - LincolnDigitalCommons@University of Nebraska - Lincoln
Kenneth Bloom Publications Research Papers in Physics and Astronomy
10-1-2001
Observation of orbitally excited Bmesons in ppcollisions at √s =1.8 TeVT. AffolderErnest Orlando Lawrence Berkeley National Laboratory, Berkeley, California
Kenneth BloomUniversity of Nebraska - Lincoln, [email protected]
Collider Detector at Fermilab Collaboration
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Affolder, T.; Bloom, Kenneth; and Collaboration, Collider Detector at Fermilab, "Observation of orbitally excited B mesons in ppcollisions at √s =1.8 TeV" (2001). Kenneth Bloom Publications. Paper 108.http://digitalcommons.unl.edu/physicsbloom/108
Observation of orbitally excited B mesons inpp collisions at AsÄ1.8 TeV
T. Affolder,21 H. Akimoto,43 A. Akopian,36 M. G. Albrow,10 P. Amaral,7 S. R. Amendolia,32 D. Amidei,24 K. Anikeev,22
J. Antos,1 G. Apollinari,36 T. Arisawa,43 T. Asakawa,41 W. Ashmanskas,7 M. Atac,10 F. Azfar,29 P. Azzi-Bacchetta,30
N. Bacchetta,30 M. W. Bailey,26 S. Bailey,14 P. de Barbaro,35 A. Barbaro-Galtieri,21 V. E. Barnes,34 B. A. Barnett,17
M. Barone,12 G. Bauer,22 F. Bedeschi,32 S. Belforte,40 G. Bellettini,32 J. Bellinger,44 D. Benjamin,9 J. Bensinger,4
A. Beretvas,10 J. P. Berge,10 J. Berryhill,7 S. Bertolucci,12 B. Bevensee,31 A. Bhatti,36 C. Bigongiari,32 M. Binkley,10
D. Bisello,30 R. E. Blair,2 C. Blocker,4 K. Bloom,24 B. Blumenfeld,17 B. S. Blusk,35 A. Bocci,32 A. Bodek,35 W. Bokhari,31
G. Bolla,34 Y. Bonushkin,5 D. Bortoletto,34 J. Boudreau,33 A. Brandl,26 S. van den Brink,17 C. Bromberg,25
M. Brozovic,9 N. Bruner,26 E. Buckley-Geer,10 J. Budagov,8 H. S. Budd,35 K. Burkett,14 G. Busetto,30 A. Byon-Wagner,10
K. L. Byrum,2 M. Campbell,24 A. Caner,32 W. Carithers,21 J. Carlson,24 D. Carlsmith,44 J. Cassada,35 A. Castro,30
D. Cauz,40 A. Cerri,32 A. W. Chan,1 P. S. Chang,1 P. T. Chang,1 J. Chapman,24 C. Chen,31 Y. C. Chen,1 M.-T. Cheng,1
M. Chertok,38 G. Chiarelli,32 I. Chirikov-Zorin,8 G. Chlachidze,8 F. Chlebana,10 L. Christofek,16 M. L. Chu,1 S. Cihangir,10
C. I. Ciobanu,27 A. G. Clark,13 M. Cobal,32 E. Cocca,32 A. Connolly,21 J. Conway,37 J. Cooper,10 M. Cordelli,12
D. Costanzo,32 J. Cranshaw,39 D. Cronin-Hennessy,9 R. Cropp,23 R. Culbertson,7 D. Dagenhart,42 F. DeJongh,10
S. Dell’Agnello,12 M. Dell’Orso,32 R. Demina,10 L. Demortier,36 M. Deninno,3 P. F. Derwent,10 T. Devlin,37 J. R. Dittmann,10
S. Donati,32 J. Done,38 T. Dorigo,14 N. Eddy,16 K. Einsweiler,21 J. E. Elias,10 E. Engels, Jr.,33 W. Erdmann,10 D. Errede,16
S. Errede,16 Q. Fan,35 R. G. Feild,45 C. Ferretti,32 I. Fiori,3 B. Flaugher,10 G. W. Foster,10 M. Franklin,14
J. Freeman,10 J. Friedman,22 Y. Fukui,20 S. Galeotti,32 M. Gallinaro,36 T. Gao,31 M. Garcia-Sciveres,21 A. F. Garfinkel,34
P. Gatti,30 C. Gay,45 S. Geer,10 D. W. Gerdes,24 P. Giannetti,32 P. Giromini,12 V. Glagolev,8 M. Gold,26 J. Goldstein,10
A. Gordon,14 A. T. Goshaw,9 Y. Gotra,33 K. Goulianos,36 H. Grassmann,40 C. Green,34 L. Groer,37 C. Grosso-Pilcher,7
M. Guenther,34 G. Guillian,24 J. Guimaraes da Costa,24 R. S. Guo,1 C. Haber,21 E. Hafen,22 S. R. Hahn,10 C. Hall,14
T. Handa,15 R. Handler,44 W. Hao,39 F. Happacher,12 K. Hara,41 A. D. Hardman,34 R. M. Harris,10 F. Hartmann,18
K. Hatakeyama,36 J. Hauser,5 J. Heinrich,31 A. Heiss,18 B. Hinrichsen,23 K. D. Hoffman,34 C. Holck,31
R. Hollebeek,31 L. Holloway,16 R. Hughes,27 J. Huston,25 J. Huth,14 H. Ikeda,41 M. Incagli,32 J. Incandela,10 G. Introzzi,32
J. Iwai,43 Y. Iwata,15 E. James,24 H. Jensen,10 M. Jones,31 U. Joshi,10 H. Kambara,13 T. Kamon,38 T. Kaneko,41
K. Karr,42 H. Kasha,45 Y. Kato,28 T. A. Keaffaber,34 K. Kelley,22 M. Kelly,24 R. D. Kennedy,10 R. Kephart,10 D. Khazins,9
T. Kikuchi,41 M. Kirk,4 B. J. Kim,19 H. S. Kim,16 M. J. Kim,19 S. H. Kim,41 Y. K. Kim,21 L. Kirsch,4 S. Klimenko,11
P. Koehn,27 A. Kongeter,18 K. Kondo,43 J. Konigsberg,11 K. Kordas,23 A. Korn,22 A. Korytov,11 E. Kovacs,2 J. Kroll,31
M. Kruse,35 S. E. Kuhlmann,2 K. Kurino,15 T. Kuwabara,41 A. T. Laasanen,34 N. Lai,7 S. Lami,36 S. Lammel,10
J. I. Lamoureux,4 M. Lancaster,21 G. Latino,32 T. LeCompte,2 A. M. Lee IV,9 S. Leone,32 J. D. Lewis,10 M. Lindgren,5
T. M. Liss,16 J. B. Liu,35 Y. C. Liu,1 N. Lockyer,31 J. Loken,29 M. Loreti,30 D. Lucchesi,30 P. Lukens,10 S. Lusin,44 L. Lyons,29
J. Lys,21 R. Madrak,14 K. Maeshima,10 P. Maksimovic,14 L. Malferrari,3 M. Mangano,32 M. Mariotti,30 G. Martignon,30
A. Martin,45 J. A. J. Matthews,26 P. Mazzanti,3 K. S. McFarland,35 P. McIntyre,38 E. McKigney,31 M. Menguzzato,30
A. Menzione,32 E. Meschi,32 C. Mesropian,36 C. Miao,24 T. Miao,10 R. Miller,25 J. S. Miller,24 H. Minato,41 S. Miscetti,12
M. Mishina,20 N. Moggi,32 E. Moore,26 R. Moore,24 Y. Morita,20 A. Mukherjee,10 T. Muller,18 A. Munar,32 P. Murat,32
S. Murgia,25 M. Musy,40 J. Nachtman,5 S. Nahn,45 H. Nakada,41 T. Nakaya,7 I. Nakano,15 C. Nelson,10 D. Neuberger,18
C. Newman-Holmes,10 C.-Y. P. Ngan,22 P. Nicolaidi,40 H. Niu,4 L. Nodulman,2 A. Nomerotski,11 S. H. Oh,9 T. Ohmoto,15
T. Ohsugi,15 R. Oishi,41 T. Okusawa,28 J. Olsen,44 C. Pagliarone,32 F. Palmonari,32 R. Paoletti,32 V. Papadimitriou,39
S. P. Pappas,45 D. Partos,4 J. Patrick,10 G. Pauletta,40 M. Paulini,21 C. Paus,22 L. Pescara,30 T. J. Phillips,9 G. Piacentino,32
K. T. Pitts,10 R. Plunkett,10 A. Pompos,34 L. Pondrom,44 G. Pope,23 M. Popovic,23 F. Prokoshin,8 J. Proudfoot,2
F. Ptohos,12 G. Punzi,32 K. Ragan,23 A. Rakitine,22 D. Reher,21 A. Reichold,29 W. Riegler,14 A. Ribon,30 F. Rimondi,3
L. Ristori,32 W. J. Robertson,9 A. Robinson,23 T. Rodrigo,6 S. Rolli,42 L. Rosenson,22 R. Roser,10 R. Rossin,30
W. K. Sakumoto,35 D. Saltzberg,5 A. Sansoni,12 L. Santi,40 H. Sato,41 P. Savard,23 P. Schlabach,10 E. E. Schmidt,10
M. P. Schmidt,45 M. Schmitt,14 L. Scodellaro,30 A. Scott,5 A. Scribano,32 S. Segler,10 S. Seidel,26 Y. Seiya,41 A. Semenov,8
F. Semeria,3 T. Shah,22 M. D. Shapiro,21 P. F. Shepard,33 T. Shibayama,41 M. Shimojima,41 M. Shochet,7 J. Siegrist,21
G. Signorelli,32 A. Sill,39 P. Sinervo,23 P. Singh,16 A. J. Slaughter,45 K. Sliwa,42 C. Smith,17 F. D. Snider,10 A. Solodsky,36
J. Spalding,10 T. Speer,13 P. Sphicas,22 F. Spinella,32 M. Spiropulu,14 L. Spiegel,10 L. Stanco,30 J. Steele,44
A. Stefanini,32 J. Strologas,16 F. Strumia,13 D. Stuart,10 K. Sumorok,22 T. Suzuki,41 R. Takashima,15 K. Takikawa,41
M. Tanaka,41 T. Takano,28 B. Tannenbaum,5 W. Taylor,23 M. Tecchio,24 P. K. Teng,1 K. Terashi,41 S. Tether,22 D. Theriot,10
R. Thurman-Keup,2 P. Tipton,35 S. Tkaczyk,10 K. Tollefson,35 A. Tollestrup,10 H. Toyoda,28 W. Trischuk,23 J. F. deTroconiz,14 S. Truitt,24 J. Tseng,22 N. Turini,32 F. Ukegawa,41 J. Valls,37 S. Vejcik III,10 G. Velev,32 R. Vidal,10 R. Vilar,6
I. Vologouev,21 D. Vucinic,22 R. G. Wagner,2 R. L. Wagner,10 J. Wahl,7 N. B. Wallace,37 A. M. Walsh,37 C. Wang,9
C. H. Wang,1 M. J. Wang,1 T. Watanabe,41 D. Waters,29 T. Watts,37 R. Webb,38 H. Wenzel,18 W. C. Wester III,10
A. B. Wicklund,2 E. Wicklund,10 H. H. Williams,31 P. Wilson,10 B. L. Winer,27 D. Winn,24 S. Wolbers,10
D. Wolinski,24 J. Wolinski,25 S. Worm,26 X. Wu,13 J. Wyss,32 A. Yagil,10 W. Yao,21 G. P. Yeh,10 P. Yeh,1 J. Yoh,10 C. Yosef,25
T. Yoshida,28 I. Yu,19 S. Yu,31 A. Zanetti,40 F. Zetti,21 and S. Zucchelli3
~CDF Collaboration!
PHYSICAL REVIEW D, VOLUME 64, 072002
0556-2821/2001/64~7!/072002~16!/$20.00 ©2001 The American Physical Society64 072002-1
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China2Argonne National Laboratory, Argonne, Illinois 60439
3Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy4Brandeis University, Waltham, Massachusetts 02254
5University of California at Los Angeles, Los Angeles, California 900246Instituto de Fisica de Cantabria, University of Cantabria, 39005 Santander, Spain
7Enrico Fermi Institute, University of Chicago, Chicago, Illinois 606378Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
9Duke University, Durham, North Carolina 2770810Fermi National Accelerator Laboratory, Batavia, Illinois 60510
11University of Florida, Gainesville, Florida 3261112Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
13University of Geneva, CH-1211 Geneva 4, Switzerland14Harvard University, Cambridge, Massachusetts 0213815Hiroshima University, Higashi-Hiroshima 724, Japan
16University of Illinois, Urbana, Illinois 6180117The Johns Hopkins University, Baltimore, Maryland 21218
18Institut fur Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany19Korean Hadron Collider Laboratory, Kyungpook National University, Taegu 702-701
Seoul National University, Seoul 151-742, Koreaand SungKyunKwan University, Suwon 440-746, Korea
20High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan21Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
22Massachusetts Institute of Technology, Cambridge, Massachusetts 0213923Institute of Particle Physics, McGill University, Montreal H3A 2T8, Canada
and University of Toronto, Toronto M5S 1A7, Canada24University of Michigan, Ann Arbor, Michigan 48109
25Michigan State University, East Lansing, Michigan 4882426University of New Mexico, Albuquerque, New Mexico 87131
27The Ohio State University, Columbus, Ohio 4321028Osaka City University, Osaka 588, Japan
29University of Oxford, Oxford OX1 3RH, United Kingdom30Universita di Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova, I-35131 Padova, Italy
31University of Pennsylvania, Philadelphia, Pennsylvania 1910432Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pias, Italy
33University of Pittsburgh, Pittsburgh, Pennsylvania 1526034Purdue University, West Lafayette, Indiana 47907
35University of Rochester, Rochester, New York 1462736Rockefeller University, New York, New York 1002137Rutgers University, Piscataway, New Jersey 08855
38Texas A&M University, College Station, Texas 7784339Texas Tech University, Lubbock, Texas 79409
40Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy41University of Tsukuba, Tsukuba, Ibaraki 305, Japan
42Tufts University, Medford, Massachusetts 0215543Waseda University, Tokyo 169, Japan
44University of Wisconsin, Madison, Wisconsin 5370645Yale University, New Haven, Connecticut 06520
~Received 3 November 1999; revised manuscript received 4 May 2001; published 4 September 2001!
We measure the relative rate of production of orbitally excited (L51) states ofB mesons (B** ) byobserving their decays intoBp6. We reconstructB mesons through semileptonic decay channels using datacollected inpp collisions atAs51.8 TeV. The fraction of lightB mesons that are produced asL51B** statesis measured to be 0.2860.06~stat!60.03~syst!. We also measure the collective mass of theB** states, andquantify the result by quoting the~model-dependent! mass of the lowestB** state to bem(B1)55.7160.02 GeV/c2.
DOI: 10.1103/PhysRevD.64.072002 PACS number~s!: 14.40.Nd, 13.20.He, 13.25.Hw
T. AFFOLDERet al. PHYSICAL REVIEW D 64 072002
072002-2
I. INTRODUCTION
The label ‘‘B** ’’ is a collective name for the four lowest-lying L51 states ofB mesons. The low-lying part of theBmeson spectrum is illustrated in Fig. 1. As a result of heavy-quark effective theory~HQET! @1#, the heavy quark de-couples from the light degrees of freedom in themb→`limit, and thus theB** states are usually labeled by the totalangular momentumj of the light quarkq, i.e., Jq5L % Sq .For theL51 states, this results in two doublets:B0* andB1*for j q5 1
2 , andB1 andB2* for j q5 32 . The states within each
doublet should be degenerate in mass by HQET and have thesame total strong-interaction width. The 1/mb correctionsturn out to be significant and break this degeneracy. Thestates in thej q5 1
2 doublet are expected to be broad sincethey can decay through anS-wave transition, whereas thej q5 3
2 states decay through aD-wave transition and aretherefore thought to be narrow.
The motivation for studying theB** states is twofold.First, the combination of a heavy and a light quark is theclosest QCD analogue of the hydrogen system in QED and istherefore an interesting testing ground for nonperturbativetheoretical models. Second, theB** states are expected todecay strongly intoBp6, so the charge of the pion fromtheir decay can be used to determine the flavor of the weaklydecayingb quark at the time of its production. By ‘‘flavor’’
we mean whether the bottom quark involved is ab or bquark, the common terminology adopted inB0 mixing andCP-violation studies. This mechanism contributes to theBflavor-tagging technique proposed in Ref.@2# and success-fully employed in Refs.@3–6#.
Early theoretical predictions@7# of the masses and thewidths for these states were obtained by extrapolation fromthe measured properties of other heavy-light quark systemsbased on the gross features of heavy-quark symmetry@1#.Calculations in the nonrelativistic valence-quark approxima-tion @8# and the fully relativistic light-quark model@9# havealso become available. The latter model is in good agreementwith the properties of the observed heavy-light mesons andheavy quarkonia. The predictions of the three approaches arelisted in Table I. To date theB** states have been observedonly in thee1e2 environment at LEP@10–13# with proper-ties in reasonable agreement with the expectations.
In this paper we present a measurement of the productionrate and the mass of theB** states using a sample ofBmesons partially reconstructed through their semileptonic de-cays into charm mesons. The data were collected with theCollider Detector at Fermilab~CDF! at the Tevatronpp col-lider. This analysis is closely related to that of Ref.@5#, and anumber of results presented there are not repeated here.
The remainder of this paper is organized as follows: Sec-tion II gives a brief overview of the CDF detector and thedetails of data selection andB** reconstruction; Sec. III liststhe backgrounds to theB** signal; Sec. IV A explains thefitting procedure and links in the treatment of the most im-portant backgrounds; the results and estimated uncertaintiesare presented in Sec. IV B; and finally Sec. V contains asummary.
II. THE CDF DETECTOR AND DATA SELECTION
A. Apparatus
This analysis was performed on the data collected withthe CDF at the Tevatron collider during the 1992–1996 data-taking period. The integrated luminosity of this data sampleis 110 pb21 of pp collisions atAs51.8 TeV. A full descrip-tion of the detector can be found in Refs.@14#, @15#. Here wedescribe briefly only the subsystems relevant to the analysis.
We use a cylindrical coordinate system with thez axispointing along the beam direction. The polar angleu is mea-sured from the direction of the proton beam, and the azi-muthal anglef from the horizontal plane. The pseudorapid-ity, h52 ln@tan(u/2)#, is frequently used in place of thepolar angle. Some quantities are measured only in the planetransverse to the beam line; these are denoted with the sub-script ‘‘T,’’ e.g., pT5p sinu is the transverse momentum of aparticle andET5E sinu its transverse energy.
The tracking systems are located inside a superconductingsolenoid, which generates a 1.4 T magnetic field. The siliconvertex detector~SVX! @15# is a solid-state tracking devicelocated immediately outside the beam pipe. It consists offour layers of silicon microstrip detectors at radii rangingfrom 3.0 to 7.9 cm. The SVX provides a measurement of theimpact parameter of tracks in the plane transverse to thebeam axis with a resolution ofsd5(13140/pT) mm, wherepT is in GeV/c; it does not measure the longitudinal coordi-nates of tracks. The outermost tracking device is the centraltracking chamber~CTC!, a drift chamber providing a three-dimensional measurement of tracks in the regionuhu,1.1from the nominalpp interaction point. The combined SVX-CTC system enables us to measure transverse track momentawith the resolution dpT /pT'A(0.9pT)21(6.6)231023,wherepT is in GeV/c. Between the SVX and the CTC lies aset of time-projection chambers measuring the longitudinalpositions of thepp interaction vertices.
FIG. 1. Predicted spectrum and dominant decays of the low-lying B meson states.
OBSERVATION OF ORBITALLY EXCITED B MESONS . . . PHYSICAL REVIEW D 64 072002
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The calorimeters are situated outside the solenoid, andconsist of ‘‘towers’’ pointing to the interaction region. Eachtower covers 15° inf and 0.1 inh. The central electromag-netic calorimeter (uhu,1.1) is an 18 radiation length lead-scintillator stack with a proportional chamber for measure-ment of the transverse shower profile. Its position resolutionis about 2 mm, and the energy resolution isdET /ET
5A(13.5%/AET)21(2%)2, whereET is in GeV. Outside itis the iron scintillator central hadronic calorimeter, which is4.5 interaction lengths thick and provides measurements witha resolutiondET /ET5A(50%/AET)21(3%)2, whereET isagain in GeV.
The central muon chambers~CMU’s! are located outsidethe calorimeters and cover the regionuhu,0.6 with 85%coverage inf. Beyond the CMU there is an additional ab-sorber of 60 cm of steel followed by the central muon up-grade chambers~CMP’s! ~uhu,0.6 with 65% coverage!.Both are made up of four layers of drift chambers.
The CDF detector has a three-level triggering system. Thefirst two levels are hardware triggers, and the third is a soft-ware trigger derived from the off-line reconstruction code.The events used in this analysis satisfied triggers that requireeither an electron of high energy~calorimeter depositionabove ET;8 GeV and an associated track abovepT;7.5 GeV/c! or a muon of high momentum~pT above;7.5 GeV/c!.
For the simulation needs of this analysis, we use thePYTHIA 5.7/JETSET7.4 generator@16# with several of its pa-rameters adjusted to achieve a good description of charged-particle multiplicities of bb events produced inpp colli-sions. The tuning procedure is summarized in Sec. III B 1.This analysis is, however, not particularly sensitive to thetuning. The generatedB mesons are decayed using the theCLEO QQB-decay Monte Carlo program@17#, and the result-
ing events passed through the standard CDF detector simu-lation.
B. Data selection
1. B candidate selection
We search for the semileptonic decay ofB mesons into anelectron or muon~which is the basis of the trigger!, a neu-trino, and aD (* ) meson. TheD (* ) is reconstructed in severalhadronic decay modes. The topology of a representativesemileptonicB decay is shown in Fig. 2. We reconstruct thefollowing ‘‘decay signatures’’ for ourB meson samples:1
~a! B1→n l 1D0, D0→K1p2,
~b! B1→n l 1D0, D0→K1p2p1p2,
~c! B0→n l 1D2, D2→K1p2p2,
~d! B0→n l 1D* 2, D* 2→D0ps2 , D0→K1p2,
~e! B0→n l 1D* 2, D* 2→D0ps2 , D0→K1p2p1p2,
~ f! B0→n l 1D* 2, D* 2→D0ps2 , D0→K1p2p0,
where the pion from theD* 2 decay is denoted asps2 to
distinguish it from others in the decay sequence. We refer toeach of these as a ‘‘decay signature’’ since they represent theexperimental selection process, which in turn results in sub-samples that are not exclusively composed of the listed se-quence of decays. One decay chain of aB meson may mimicanother if particles are missed in the reconstruction. For ex-ample, theB0 decay sequence written for signature~d! willcontribute to the event subsample of~a! if the ps
2 from theD* 2 decay fails the reconstruction criteria. In general, if acharged particle is missed in the reconstruction, the apparentB charge is changed, and charged and neutralB meson de-cays will thereby cross contaminate each other’s signatures.The contamination between charged and neutralB mesons isrelatively modest, not more than 20% for any of the signa-tures in this analysis. The separation is aided by the fact thatthe first two signatures ofl 1D0 have candidates removed ifthey are also validl 1D* 2 candidates.
1Use of specific particle states in this paper implies the use of thecharge-conjugate states as well.
FIG. 2. Topology of a semileptonicB decay. Measurable par-ticles are shown as solid lines. The particles ‘‘~X!’’ originating at thesecondary vertex may come from the decays of excited states ofDmesons or fromB→n lDX decays.
TABLE I. Predicted properties ofB** mesons.
Name J j q
Mass (GeV/c2)
Width DecaysRef. @7# Ref. @8# Ref. @9#
B0* 0 12 5.870 5.738 broad (Bp)L50
B1* 1 12 5.875 5.757 broad (B* p)L50
B1 1 32 5.759 5.700 5.719 narrow (B* p)L52
B2* 2 32 5.771 5.715 5.733 narrow (Bp,B* p)L52
T. AFFOLDERet al. PHYSICAL REVIEW D 64 072002
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The sample selection is the same as Ref.@5# except for theaddition of thel 1D0, D0→K1p2p1p2 signature, whichincreased the sample of chargedB mesons by nearly 60%.The reader may refer to this previous work for details of theB candidate selection; we only outline the approach here andsummarize the kinematic and geometric selection criteria inTable II.
The tracks of theD (* ) daughters must lie within a cone ofDR[A(Dh)21(Df)251.0 around the lepton, and exceed apT threshold~see Table II!. All tracks ~except one in the caseof D0→K1p2p2p1! must use SVX information, and theymust also be consistent with originating in the vicinity of thesame primary vertex. The candidate tracks must form a massin a loose window around the nominalD mass, where allpermutations of mass assignments, consistent with the charmhypothesis, are attempted. The candidate tracks are thencombined in a fit constraining them to aD decay vertex, andx2 and mass window cuts are imposed. We require theDtracks to be displaced from the primary vertex based on thetrack impact parameter significanced0 /s0 , whered0 is theimpact parameter in the transverse plane with respect to theprimary vertex ands0 is its error. The specific requirementdepends upon the decay signature, as listed in Table II. Theprojected transverse distanceLxy(D) between theD vertexand the primary vertex must be greater than its uncertaintysLxy
@Lxy(D)/sLxycut in Table II#. We next find theB vertex
by projecting theD back to the lepton track, and their inter-section determines theB vertex, as sketched in Fig. 2. If thereconstruction includes aps
2 from a D* 2 decay, theps2 is
used to further constrain theB vertex. A loose cut is appliedto theD proper decay length relative to theB vertex~ctD cutin Table II!. Some further demands on masses or mass dif-ferences are summarized in Table II. Finally, the lepton andthe charm candidates are required to be consistent with the
decay of a singleB, i.e., the signal must have al 1K1 orl 2K2 correlation.
Figure 3 shows the charm candidate mass distributions forthe six reconstructedB signatures. The solid~dashed! histo-grams in the figure are the distributions of the candidateswith the right~wrong! l 2K charge correlation coming froma singleB meson. The wrong-sign distributions show no ex-cess at the appropriate charm mass, indicating that the right-sign distributions are clean samples of semileptonicB de-cays. The numbers ofB candidates for each decay signature,summarized in Table III, are determined by sideband~hatched regions in Fig. 3! subtraction. This is a straightfor-
ward procedure except for theD0→K1p2p0 signature~f!,where we use the shape of the wrong-sign mass differencedistribution ~dashed histogram! renormalized to the~hatched! right-sign sideband region. The selections result ina total of almost 10 000 partially reconstructedB mesons.
2. B** candidate reconstruction
A B** candidate is constructed by combining aB candi-date with any track compatible with originating from theprimary interaction vertex—generally referred to as a‘‘prompt’’ track. We assume that every such track was pro-duced by a pion since we do not efficiently distinguish par-ticle species. The tracks are required to be reconstructed inthe SVX for precision measurement of the impact parameter,and have an impact parameter that is less than 3.0 standarddeviations from the primary vertex. Furthermore, only trackswith transverse momentum greater than 900 MeV/c are used.This value was determined from the Monte Carlo simula-tions in order to maximize the significance of the anticipatedB** signal.
TABLE II. Event selection criteria for the six decay signatures. The cut on the impact parameter significanced0 /s0 is applied toDdaughter tracks only.Lxy(D)/sLxy
is the transverseD decay length significance relative to the primary vertex, whilectD is the proper decaylength of theD with respect to theB vertex.Dm(D* ) is the mass difference between theD* candidate and theD candidate plus the chargedpion mass.
Selection cuts
Decay signatures
lD 0 lD 2 lD * 2
K1p2 K1p2p1p2 K1p2p2 K1p2 K1p2p1p2 K1p2p0
pT( l ). (GeV/c) 6.0 6.0 6.0 6.0 6.0 6.0pT(K). (GeV/c) 0.7 0.8 0.6 ¯ ¯ 1.0pT(p). (GeV/c) 0.5 0.6 ¯ ¯ ¯ 0.8pT(D). (GeV/c) 2.0 3.0 3.0 ¯ ¯ ¯
d0 /s0. 3.0 ¯ 2.0 1.0 0.5 1.0Lxy(D)/s l xy
. 3.0 3.0 5.0 1.0 1.0 1.0uDm(D* )u, (MeV/c2) ¯ ¯ ¯ 3.0 2.0 ¯
m( lD ), (GeV/c2) 5.0 5.0 5.0 ¯ ¯ ¯
20.5,ctD, ~mm! 1.0 1.0 2.0 1.0 1.0 1.5um(p1p2)2m(r0)u, (GeV/c2) ¯ 0.15 ¯ ¯ ¯ ¯
um(K1p2)21.5u, (GeV/c2) ¯ ¯ ¯ ¯ ¯ 0.2
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The missing neutrino from the semileptonicB decay pre-vents us from fully reconstructing theB meson.2 Our resolu-tion on the mass of theB** candidates is thereby impairedby the unknown momentum of the neutrino. The kinematicsof the B meson decays in our sample are determined mostlyby the acceptance of the lepton triggers and, to a lesser ex-tent, by the selection requirements on the hadronicD decayproducts. The relatively high momentum threshold of thelepton triggers biases the neutrinos of thoseB mesons enter-ing our sample to possess a fairly modest fraction of the fullB momentum. As a result, on average, the reconstructedBdecay products comprise about 85% of the trueB momentum~averageB transverse momentum is;21 GeV/c!, and havean rms spread about the mean of;10%.
The mass resolution of the reconstructedB** candidatescan be improved by correcting the measured momentum ofthe visibleB decay products to account for the loss of theneutrino. An average multiplicative correction factor for eachdecay signature, determined by Monte Carlo simulation, isapplied on an event-by-event basis to the momentum of thereconstructedB candidate as a function of the mass of thevisible B decay products. Instead of using the direction of thevisible B momentum, the transverse direction of theB mesonis deduced from theB production and decay vertices for afurther improvement in theB** mass resolution.
Despite these corrections, the smearing of theB** candi-date masses, due to the missing neutrino, is still severe. In-stead of looking for aB** →Bp6 peak in the mass distri-bution, we use the mass differenceQ[m(Bp)2m(B)2m(p), where the reconstructed mass of theB candidates isused. Some of the smearing effects within an event cancelfor this quantity. The resolution ofQ is, however, also af-fected by the decays of theB** to B* , since we do notreconstruct the soft photon fromB* →Bg. Furthermore,only two of the B** states are expected to be narrow(;20 MeV/c2), while the other two, making up one third ofall B** states by spin counting, should be broad(;100 MeV/c2) @7#. Monte Carlo studies indicate that the
TABLE III. The numbers ofB candidates in the signal regions and the estimated numbers ofB mesonsafter background subtraction for each decay signature.
Signature Candidates B mesons
~a! D0→K1p2 3141 2668653
~b! D0→K1p2p1p2 3404 1534649
B1 signatures total 6545 4202673
~c! D2→K1p2p2 2275 1454643
~d! D* 2→D0ps2 , D0→K1p2 891 835629
~e! D* 2→D0ps2 , D0→K1p2p1p2 618 524623
~f! D* 2→D0ps2 , D0→K1p2p0 4288 2678659
B0 signatures total 8072 5491682
2TheB decay signatures include contributions fromB→n lD ** decays, for which the pion or photon fromthe D** decay chain is also missing. The kinematic effects of these other missing particles are implicitlyincluded when referring to the ‘‘neutrino,’’ which is usually the dominant source of missing momentum.
FIG. 3. Mass distributions of theD (* ) candidates for the sixBdecay signatures~see the text for the alphabetical signature labels!.
The last signature~f! is for D0→K1p2p0, where thep0 is not partof the reconstruction, and the mass difference between the visible
D* 2 and D0 decay products is plotted instead of the mass. Thesolid histograms are for the candidates that have the correct chargecorrelation forB decays (l 6K6), and the dashed histograms for theopposite correlation. The hatched regions are the sidebands used forbackground subtraction. The yields ofB mesons are summarized inTable III.
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resolution ofQ for B** decays, in spite of these resolution-limiting effects, is around 50 MeV/c2 with no significant sys-tematic shift after correcting the visibleB momentum.
The charge of the pion from aB** decay always matchesthe light quark content of the associatedB meson, i.e.,B**mesons decay intoB1p2 or B0p1, as shown in Fig. 4, andnever toB1p1 or B0p2. We label the correctB1p2 andB0p1 pairings as ‘‘right sign,’’ and the unphysical decaycombination as ‘‘wrong sign.’’ It is important to note thatBmesons with the sameb flavor ~e.g., B1 and B0! have theoppositedefinition for the right-sign pion charge, i.e.,p1 forB0 andp2 for B1. If one knew, without fail, the flavor andcharge state of theB meson at the time of creation, theB**would appear as an excess in the right-signQ distributionsonly. In our sample, however, we expect some cross con-tamination between flavors throughB02B0 oscillations andincomplete reconstruction of all of theB decay products, asexplained later in the paper.
A further complication is present. The particles producedin the hadronization ofb quarks intoB mesons are also ex-pected to form low-mass combinations with theB candi-dates, and to favor the same right-sign correlation as inB**decays. Thus, the primary experimental difficulty in thisanalysis is to separate the~broad! resonantB** signal fromthe low-mass nonresonant hadronization background, whichalso favors the same right-sign charge correlation.
The Q distributions of ourBp6 candidates are shown inFig. 5. These areinclusivedistributions, meaning that we donot choose only one candidate track perB, otherwise biasesmay be introduced that are difficult to calculate. Any trackthat satisfies our selection criteria enters into these distribu-tions, so there may be multipleB** candidates perB candi-date. There is a clear right-sign excess at lowQ, but as al-luded to above, the background~e.g., wrong-sign candidates!peak in the same region, and the behavior is quite differentfor the charged and neutral signatures. We next consider thevarious contributions to Fig. 5, and disentangle theB** sig-nal from the charge correlated and kinematically similar had-ronization background in the data.
III. B** BACKGROUNDS
The backgrounds to a potentialB** signal can be dividedinto two broad classes. We refer to those produced in asso-ciation with theb quark, and which are therefore dependenton its charge and momentum, as ‘‘correlated’’ backgrounds.Those that are independent of the presence of heavy quarksin the event are ‘‘uncorrelated’’ backgrounds. We sidebandsubtract the uncorrelated backgrounds directly in the data,
whereas the correlated ones, especially the one coming fromhadronization tracks around theB meson, require a moreinvolved treatment.
A. Uncorrelated backgrounds
Three sources of uncorrelated background contributionsare taken into account: fakeB meson candidates, ‘‘pile-up’’events, and particles from the ‘‘underlying’’ event. All threecomponents are measured from the same data sample that isused for this analysis, and their contributions are subtractedbefore theB-p candidates are analyzed further.
The combinatorial background in the reconstruction of theD (* ) mesons results in fakeB meson candidates under theD (* ) mass peaks. We divide the mass spectrum ofD (* ) can-didates into signal and sideband regions~shown in Fig. 3!,and perform a sideband subtraction on theQ distribution ofthe B** candidates. This subtraction is performed indepen-dently for eachB meson signature. This procedure yields theB-p Q distributions for trueB mesons, but there are otherbackgrounds to aB** signal that must be considered.
At the higher Tevatron luminosities, it is not unusual tohave multiple hardpp collisions in the same beam crossing,which we refer to as event ‘‘pile up.’’ The spatial resolutionof the tracking detectors is on the order of a centimeter alongthe beam~z! axis, whereas the collisions have a correspond-ing ;30 cm rms spread around the center of the detector. Itis usually possible to distinguish which tracks arise fromwhich interaction, but occasionally a secondary collision willoccur so close inz to the one that produced theB meson thatthe two cannot be distinguished. In the latter case, we willsometimes formB** candidates using pions frompp inter-actions unrelated to the one that produced theB meson.
We correct for this effect by looking at the distribution oftracks well separated from theB vertex and then extrapolateinto the region where we are unable to resolve additionalvertices close to theB. We first determine the distribution ofthe spatial separations (Dz) along the beam line between theB production vertex and thez coordinate of tracks in theevent~i.e., thez coordinate of the point of closest approach
FIG. 5. TheQ distributions of theBp6 candidates in the datasummed over the charged~left! and neutral~right! B signatures. Thecandidates with the right~wrong! B-p6 charge correlation areshown as solid~dashed! histograms.
FIG. 4. An idealized picture of the decays ofB** mesons intoBmesons and charged pions illustrating the pion charge correlationswith the constituent quark types.
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of the track helix to the beam line!. This distribution, shownin Fig. 6~a!, has a narrow peak atDz50 that is composed oftracks coming from the same interaction as theB meson andthat has a width characteristic of thez resolution of the de-tector. This peak lies on top of a broad Gaussian-like distri-bution of tracks coming from other~uncorrelated! pp inter-actions in the same beam crossing. From the fitted curves inFig. 6~a!, the pile-up background accounts for about 5% ofthe total tracks we associate with theB production vertex inthe B** reconstruction. We define a signal region (uDzu,5 cm) and choose sidebands@hatched regions in Fig. 6~a!#
to produce aDz sideband subtractedQ distribution of theB-p candidates.
The final uncorrelated background component we takeinto account is that from the particles of the ‘‘underlyingevent.’’ In most pp collisions, any heavy flavor producedaccounts for only a fraction of all particles emanating fromthe collision. The remaining particles are the product of ra-diation of the remnants of the original~anti!proton. Theseparticles are expected to be uncorrelated with the direction ofthe b jets, and therefore isotropic in the plane transverse tothe beam. We tested this assumption by verifying that theazimuthal distribution of particles relative to the recon-structedB meson over 0,uf~track!2f(B)u,2 is uniformin the uDhu[uh~track!2h(B)u.1 region.3
We correct for this underlying track background by againdoing a variant of the sideband-subtraction procedure. Thedistribution of azimuthal separations between charged par-ticles and the reconstructedB mesons withuDhu,1, shownin Fig. 6~b!, reveals that most of theb jet associated with theB meson is confined to the regionuDfu,0.8. One sees fromFig. 6~c!, consistent with this observation, that the rightwrong-sign asymmetry vanishes outside this ‘‘B’’ region ofuDfu,0.8. The uniform distribution in the 1,uDfu,2 re-gion is presumed to be dominated by the underlying eventparticles, and we use the properties of these tracks to esti-mate the contribution of the underlying event particles to theQ distribution. This is accomplished by rotating these tracks@hatched ‘‘sideband’’ in Fig. 6~b!# in the transverse plane‘‘under’’ the B meson, i.e., reducing theiruDfu by 1. We thensubtract theQ distribution of these ‘‘sideband’’ events fromthe rawB-p Q distribution to remove the effect of the un-derlying event background from theB** candidates.
The Q distribution of theB** candidates, which resultsafter these three backgrounds have been subtracted from theraw distribution~Fig. 5! is shown in Fig. 7. A clear right-signexcess remains, but one still may not interpret this excess asa B** signal.
B. Correlated backgrounds
The correctedQ distributions in Fig. 7 consist predomi-nantly of combinatoric background formed from realB me-sons combined with hadronization particles from the forma-tion of the B meson, and the~potential! B** signal. Themain difficulty in this analysis lies in making a robust dis-tinction between these two components as they both havesimilar kinematic characteristics and a preference for theright-sign B-p correlation. We use a Monte Carlo inspiredparametrization, constrained by the data, as a model for theQ distribution of the hadronization background. This ap-proach to modeling the hadronization background is found tobe fairly insensitive to the details of the simulation.
3We restrict the azimuthal range because the uniformity is spoiledas uDfu approachesp by the tracks coming from the jet associatedwith the otherb hadron in the event. This other jet tends to beback-to-back inf with respect to theB meson, but is largely un-correlated to it inh.
FIG. 6. Background track distributions:~a! The Dz distributionbetween theB meson’s production vertex and other tracks in theevent for data~histogram!, and a parametrized fit to the data~solidcurve!. ~b! The azimuthal distributionDf of tracks with respect tothe B meson direction foruDhu,1, right- and wrong-signB-ppairs, are plotted separately.~c! The azimuthal distribution for theright-sign excess.
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1. Hadronization particles
Hadronization particles are those resulting from the QCDprocesses that form a color-neutral meson from ab quark.All the B** analyses published to date@10–13# rely onMonte Carlo calculations to predict the shapes of eitherQ ormass [email protected]., n(Q)[dN/dQ or dN/dm# for thisbackground. We found that the available Monte Carlo eventgenerators poorly describe the complex environment of ahadron collider in this respect. For this reason we sought toconstrain the shape of this background from the data andthereby reduce the dependence of the results on the hadroni-zation model implemented in a given simulation.
A simple approach would be to parametrize the shape ofthe Q distribution arising from the hadronization tracks, fitthe parametrization to the wrong-signBp combinations@nWS(Q)# of Fig. 7, and subtract the same distribution fromthe right-sign candidates@nRS(Q)#. This is, however, incor-rect since one does not expect the right-sign and the wrong-sign hadronization components to have the same magnitude.
A mechanism believed to be responsible for such a differ-ence is illustrated in Fig. 8: as ab quark hadronizes, it‘‘pulls’’ quark-antiquark pairs out of the vacuum, and thefirst charged pion in the hadronization chain carries a chargecorrelated with the flavor of the bottom quark. This is thesame correlation present inB** decays, namely,B1p2 andB0p1. Pions that form as direct~or near direct! neighbors tothe B meson in the~naıve! hadronization chain are expectedto have velocities similar to theB, and they will thus prefer-entially result inBp pairs with lowQ values similar toB**decays. While this simple qualitative argument does not en-compass the full complexity of the hadronization process, theexpected correlation trends have been observed in data by
several experiments@3–5,10#.4 One must, therefore, care-fully correct the observedQ distributions for the hadroniza-tion excess of right-sign over wrong-sign particles.
In dealing with the hadronization background, it is conve-nient to change variables from the right- and wrong-signdistributions,nRS(Q) and nWS(Q), to an equivalent set ofvariables: the total distributionn(Q)5nRS(Q)1nWS(Q) andthe correlation asymmetry
A~Q
tuned and default values, but in the opposite direction. Thevalues of the other tuning parameters are then determined byreadjusting them to obtain the best match—by the same pro-cedures used in the original tuning—between the overtunedsimulation and the data. The shift inspT
frag between the tuned
and the extreme values is more than an order of magnitudelarger than the ‘‘1s’’ uncertainty estimated from the originaltuning of the Monte Carlo. We quantify the simulation un-certainty by using this much larger shift to be conservative.The tuned simulation is then used for our nominal descrip-tion of hadronization particles, and the default and overtunedsimulations are used as our 1s variations.
The predicted asymmetries of the hadronization particlesare shown in Fig. 9 for all three sets of parameters. Overall,they have quite differentQ distributions, but, significantly,the asymmetries arenot very sensitive to the Monte Carloparameters in thelow-Q region, where we expect theB**signal to be. The divergent behavior at high-Q has little bear-ing on our result since very few hadronization particles areproduced in that region and this corresponds to masses abovethe region of interest. The asymmetries for charged and neu-tral B mesons are also seen to behave differently,5 and there-fore the charged and neutral composition of the various~im-pure! B decay signatures requires careful treatment~Sec.IV A !.
In addition to the asymmetryAHA(Q) we need the totalnumber distributionn(Q) of the hadronization background
to completely describe the data. In order to further insulateour results from the simulation, we do not rely upon theMonte Carlo to determine this distribution, but we insteadused the simulation as a guide to formulate a parametrizationof the shape ofn(Q) and use the data to fit for the freeparameters. We empirically found that
n~Q!5N exp~2Q/W!QR ~2!
well described the shapes of the different Monte Carlo simu-lations. Fits of this parametrization to the simulated distribu-tions indicate that the various subsamples do not prefer sig-nificantly different values ofR. This parameter is also highlycorrelated with the ‘‘width’’W in the fits, and varying bothR and W amounts to overparametrizing theQ distribution.For these reasons, we fixR to its tuned Monte Carlo value.Furthermore, the widths~W! of the distributions for chargedand neutralB hadronization particles were indistinguishablefor a given set ofPYTHIA parameters, which we exploit byimposing this as a constraint in our model.
We therefore describe the hadronizationQ distributions inthe data by the parametrization of Eq.~2! with separate nor-malizationsNu and Nd for charged and neutral mesons, acommon widthW, and the fractional excessAHA(Q) ofright-sign over wrong-sign tracks fixed to the tuned asymme-try distributions in Fig. 9. We do not rely upon the simulationto determine the values of the threen(Q) parameters, ratherthey are constrained by the data by allowing them to float inthe fits of the measuredQ distributions when extracting theB** signal in Sec. IV B. We thus reduce our dependence onthe specific hadronization model employed in the simulationto the tunedPYTHIA asymmetry dependence, while using thedefault and the overtuned distributions to estimate the sys-tematic uncertainty due to the asymmetry constraint.
2. Other correlated backgrounds
There remain a few potential backgrounds that are notaccounted for so far. The sideband subtractions of theD (* )
mass distributions~Sec. III A! remove fakeD (* ) back-grounds, and the absence of a signal in the wrong-sign( l 6K7) charm mass distributions~see Fig. 3! means random~possibly fake! leptons paired with realD (* ) mesons arerare. Other backgrounds that may be biased toward the cor-rect l 6K6 correlation are, however, not accounted for by thismass sideband subtraction. There are several physical pro-cesses that can mimic the correct correlation and must still beconsidered. In contrast to the previously described back-grounds, we do not handle these by sideband subtraction, butinstead fold in their charge correlatedQ distributions as partof the B** fit discussed in Sec. IV.
A significant fraction ofB mesons in our sample decaythrough D** mesons. The pions from subsequentD**→D (* )p6 decays originate at the secondary vertex~see Fig.2!, but some fraction of them will be consistent with havingcome from the primary vertex and possibly pose as pionsfrom B** decays. The charge of these pions is fully corre-lated with theB flavor. We do not attempt to reconstruct theD** states, and requiring all candidate tracks to be incom-patible with originating from the secondary vertex, signifi-
5Studies comparing data to simulation@5# indicate that these dif-ferences are due to the fact that the hadronization process producesa differentp1/K1/p mix for B0 compared toB1. For example, thegeneralization of the naı¨ve picture of Fig. 8 results in the correlationthat aB1 will be accompanied by aK2 ~which we treat asp2!,
whereas theB0 is accompanied byK0, which is lost to ourB**reconstruction. The Monte Carlo simulation predicts that kaons ac-count for nearly two-thirds of the hadronization difference betweenB1 andB0, and the remainder is caused by protons.
FIG. 9. Asymmetries of theb hadronization particles associatedwith the two meson types, as produced by thePYTHIA/JETSETMonteCarlo generator. The three sets of curves were produced using dif-ferent sets of generator parameters~see the text!, our nominal de-scription is given by the ‘‘tuned’’ set. The definition of right-signcorrelation depends on the flavor of the meson, i.e., positive asym-metry aroundBu(Bd) means an excess ofp2(p1).
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cantly reduces the acceptance forB** candidates. To ac-count for this effect, we add the predicted contribution of theD** pions to the other background distributions when cal-culating theB** production fraction. The magnitude of thiscontribution is a function of branching ratios and detectionefficiencies.6
We also consider the effect ofBs** →B1K2 decays. Herethe kaons—which are not experimentally distinguished frompions—do come from the primary vertex, and therefore con-tribute to the sample ofB** candidates. TheQ shape of thiscontribution is determined from a Monte Carlo calculationusing theBs** mass spectrum predicted in Ref.@9#. For therate ofBs** production relative toBs , we use theB** to Bproduction rate scaled by the relativeBs
0 to Bd0 rates. TheBs
0
to Bd0 rate is obtained from the measured ratio of the had-
ronization probabilitiesf s / f d50.3060.07 @20#, with a fur-ther correction for theBs** →BK feed down. TheB** pro-duction rate is one of the unknown parameters we aredetermining, so theBs** rate is expressed as a function of thefloatingB** rate as well as thef s / f d constraint in the even-tual fit. The charged kaon background is only associated withchargedB mesons, butBs** decays also contributeBd
0 me-sons to the samples throughBs** →B0K0 decays. These ef-fects, which contribute a few percent to the sample size, arealso included in the fitting process.
Finally, higher-order heavy flavor production may alsocontributeB-p candidates to our sample. In particular, gluonsplitting to cc or bb can result in both heavy quarks beingnear each other and give rise to correlations that may affectthe analysis. TheB→ l 1D (* )X signal can be contaminatedby g→cc when the lepton comes from one charm hadronand the other was reconstructed as aD (* ). The correctl 6K6
charge correlation is present to enter theB sample, but theseevents rarely pass the selection criteria. Constraints obtainedfrom the data have shown that thiscc contribution is negli-gible @5#.
On the other hand,g→bb production is potentially a con-cern since our procedure for subtracting the underlying event
contribution assumes that there are no decay products of theotherb quark—whose charge is correlated with the detectedB meson—in the azimuthal region of the detector perpen-dicular to theB meson [email protected]., the 1,uDfu,2 side-band region of Fig. 6~b!#. In this case the decay products oftheb hadron will bias the background subtraction and distortthe Q distributions. To account for this effect, we generatedevents using thePYTHIA program, but reweighted them toagree with thebb azimuthal distributions of a next-to-leading-order QCD calculation@21#. From these events, wedetermined the shape of the charge-correlatedQ distributionsto model theg→bb contribution, and add it into the back-ground mix used later in the fit. The rate of this process is notwell known; to be conservative we assume it contributes afraction of 30%, with an uncertainty equal to its full value.We found this uncertainty to have a very small effect on theprecision of the final results.
IV. EXTRACTING THE B** PRODUCTION FRACTION
The observed right- and wrong-signB-p Q distributions~Fig. 7! are composed of weighted averages of differenttypes ofQ distributions: those fromB** decays,B1 andB0
mesons plus hadronization particles, and some residual phys-ics backgrounds~Sec. III B 2!. The weights for each type ofcontribution are determined by the relative detection effi-ciencies and decay branching ratios of the decay chains in-volved. Knowledge of these, and the shapes of the variousQdistributions, enables one to extract theB** component bycomparing these expectations to the observedQ distributionsin the data.
To obtain theB** production fraction, we perform abinnedx2 fit of the ensemble ofQ distribution shapes to thebackground-corrected distributions of Fig. 7. The relativeweighting factors of each contribution are, however, compli-cated by the fact that there are a large number of decaychains contributing varying amounts of ‘‘cross talk’’ betweenB0 and B1 decay signatures. A map of the decay chains isshown in Fig. 10, and the cross talk between the upper andlower halves of the diagram must be unraveled before aB**signal can be extracted.
A. Fitting the Q distributions
To describe the origin and characteristics ofB-p candi-dates, we consider all the possible decay chains that contrib-ute to theB signatures, the sources of all charged particles
6We usef ** 50.3660.12 as the fraction of semileptonicB decaysto D** states~derived from CLEO measurements@19#!. For therelative branching fraction (PV) of D** →D* p, appropriatelyweighted forB mesons decaying into the four differentD** states,we use 0.3360.28 as previously measured in this same sample@5#.Reconstruction efficiencies are determined by simulation.
FIG. 10. Diagram of decay transitions con-tributing to the l 2D (* ) samples. The left-handside portrays the strong decays of excitedB me-sons to the ground state, the weak semileptonicdecays of theB0,1 occur in the middle, and theright-hand side shows the decay paths of the vari-ous charm mesons that result.
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that are paired with theB candidates, and importantly, pre-serve the kinematic and charge correlations between them.
We first consider the hadronization particles, schemati-cally arising on the far left side of Fig. 10. The nature of thehadronization particles is specific to the charge state of theassociatedB(* ,** ) meson.7 The Q distribution nu(Q) de-scribing the hadronization products associated with a bottommeson containing au quark, is different from the distributionnd(Q) for the production of one with ad quark. A puresample of a particular ground-state bottom meson, sayB0,arises from the production ofB, B* , andB** mesons. TheB-p hadronization distribution for directly producedB0 me-sons isnd(Q), but B0 mesons arising fromB** 1→B0p1
decays will follownu(Q) instead. This results in one type ofa cross talk, i.e., a pure sample ofB0 mesons has a mixtureof both nd(Q) andnu(Q) hadronization particles. The mag-nitude of this effect depends upon theB** production frac-tion that we wish to measure.
The hadronizationQ distribution for a pure sample ofground-stateB mesons containing an ‘‘x’’ light quark is
nx8~Q!5nx~Q!aCx ~Q!1ny~Q!a I
x~Q!, ~3!
where ‘‘y’’ represents the light quark constituent of the cross-talk meson. The coefficientsa quantify the magnitude of thecross talk. For example,a I
x is the fraction of detectedBx
mesons that were produced via aBy** meson and decayedthrough a charged pion. The subscriptsC and I stand for‘‘correct’’ and ‘‘incorrect’’ association between the type~u ord! of B meson and the hadronization distribution, andaC1a I51. For this particular instance of cross talk, these co-efficients can be written
aC512h** @12~1/3!eB** #
12h** ~12eB** !, ~4!
a I5~2/3!h** eB**
12h** ~12eB** !, ~5!
whereh** is the fraction ofb quarks hadronizing into lightB mesons that areB** states—the number we wish tomeasure—andeB** is the efficiency for detecting aB mesonproduced inB** decay relative to one produced directly inthe hadronization process. The latter is a function of themasses of theB** states and is near 80% with our selectionrequirements. The factor of 2/3 is the fraction ofB** me-sons that contribute to the cross talk by decaying through acharged pion; we assume it is determined by strong isospinconservation.
The right- and wrong-signB-p correlations are conve-niently handled in terms of asymmetries@Eq. ~1!#. Given thatthe production asymmetry for anx-type meson isAx(Q), theasymmetry for theBx ground-state sample is
Ax8~Q!5Ax~Q!nx~Q!aC
x 2Ay~Q!ny~Q!a Ix
nx~Q!aCx ~Q!1ny~Q!a I
x~Q!. ~6!
Note that the asymmetries in this equation aresubtractedinthe numerator, which is a direct consequence of the fact thatthe definition of the right-signB-p correlation is opposite forthe twoB meson charge states,B1 andB0.
Equations~3! and ~6! provide the means to predict theobservedQ distributions for hadronization particles account-ing for the cross talk arising fromB** decay. We generalizethis approach by adding to the weighted averagesn8 andA8the contribution from theB** signal. This source has anasymmetry equal to11 @i.e., nWS(Q)50# and a shape deter-mined from the Monte Carlo simulation. The shape is depen-dent upon the masses of the fourB** states, but it is stronglydistorted by the kinematics of the unobserved neutrino suchthat most of the structure is washed out. Itsa weight is givenby the their relative production rateh** and detection effi-ciencyeB** . Both the production rate and the collectiveB**mass are the parameters to be determined in this analysis.
At this point we have theQ description for idealizedB0
andB1 samples. The actual samples of six decay signaturesare not pure. Samples derived fromB0 mesons will have anadditional cross talk arising fromB02B0 oscillations. Weaccount for this effect by obtaining a mixing corrected asym-metry A9 for the B0 components by multiplying the asym-metry prior to mixingA8 by the factor (122xeff), wherexeffis the probability that a reconstructed neutralB meson hasdecayed as an antiparticle of the produced one. This prob-ability depends upon the true time-integrated mixing prob-ability as well as the acceptance as a function of the propertime of B decay, and from Monte Carlo calculations it isfound to be 2161% for our data sample. Note thatB02B0
oscillations reduce the asymmetry of both theB** signaland the hadronization background, since both are correlatedwith the B mesons at the time of production, not decay.
The last instance of cross talk to account for is that be-tween the charged and neutral decay chains caused by decaysthrough the excited states ofD mesons—the right half of Fig.10. The final composition of the signal and background isgiven by formulas like Eqs.~3! and ~6!, but the coefficientsaC and a I are calculated in a more involved way from theparameters determining the relative branching ratios of thevarious decay chains and their relative reconstruction effi-ciencies following Ref.@5#.
Finally the effects of the residual correlated backgroundsof Sec. III B 2 are included. TheQ distributions obtainedfrom the simulation are introduced into the weighted averageof the asymmetry, witha weights determined by the produc-tion, decay, and acceptance of each particular process.
The full expressions describing the weights of theQ dis-tribution due to these various processes are straightforwardto derive, but they are somewhat intricate, and we do notreproduce them here as they do not aid the discussion. Someof these weights depend upon theB** fraction we seek. Thecombined effects of the various contributions to the chargecorrelatedB-p Q distributions are fit to the sideband sub-
7We assume that the hadronization particles produced in associa-tion with the excited states ofB mesons are of the same nature asthe ones around the ground state of the same charge.
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tracted distributions obtained from the data. The fit is aQ-binned x2 fit, performed simultaneously over all decaysignatures.
The composition of the background is highly correlatedwith the B** production fractionh** , which is being mea-sured, as well as with other sample composition parameters,such asf ** , xeff , andPV , that determine the magnitudes ofthe three instances of cross talk, i.e.,B** decays throughcharged pions,B02B0 oscillations, and decays through ex-cited D meson states. The fit is, therefore, generalized toinclude x2 constraints for these other external parameters.For each of these ‘‘constrained floating’’ parameters, we in-clude a termxP
2 5@(Pmeas2P)/s(P)#2 in the full x2, wherePmeasis the measured value of parameterP, ands(P) is itsuncertainty. These values are either taken from measure-ments in other experiments or determined from our data in ameasurement separate from theB** fit @5#.
This arrangement of constrained floating parameters aidsin the proper estimation of the fit errors. Estimating the sys-tematic errors due to the fixed input parameters by the com-mon practice of varying each of these parameters in turn by1s, would overestimate the total uncertainty because of thecorrelations between the parameters. On the other hand, thecorrelations are automatically accounted for by letting theparameters float. However, the fitter then returns an uncer-tainty that is the combination of statistical and systematiceffects,s total. The two classes of uncertainties are separatedby repeating the fit with all the constrained floating param-eters fixed to the values obtained from the fullx2 minimiza-tion. This reduced fit yields the pure statistical uncertaintysstat, and, in the Gaussian approximation, we obtain the sys-tematic uncertainty by subtracting in quadrature,
ssystcorr5As total
2 2sstat2 . ~7!
This systematic uncertainty only includes the effects relatedto the floating~correlated! fit parameters. Other uncertainties,external to the fit, are added in quadrature as usual.
B. Results
The right- and wrong-signQ distributions of all six decaysignatures are fit simultaneously. The variables that floatfreely ~unconstrained! in the x2 fit are theB** productionfraction (h** ) and the three parameters describing thedashed hadronization background@theBu andBd amplitudesNu and Nd , and the common shape parameterW of Eq.~2!8#. In this way we have relied upon the Monte Carlo had-ronization model to guide us in selecting a simple parametri-zation for this background, but the data determines its am-plitude and specific shape. The remainder of the parametersfloat, but are constrained to their externally measured values.
The results of the fit are shown in Fig. 11. The points arethe dataQ distributions, the dashed curves are the fitted
shapes of the hadronization component, the dotted histo-grams are the sums of all backgrounds, and the solid histo-grams are the totals including the fittedB** signal. Thecomplete set of fit parameters is listed in Table IV, includingthe input constraint values. The fit parameters that determinethe sample composition yield the values given in Table V forthe coefficients quantifying theB02B1 purity of each decaysignature. The cross contamination between these ground-state mesons amounts to no more than 20% in any signature.The fraction ofBs** mesons contributing to the sample, de-termined by the sample composition fit parametersf s / f d ,h** , andeB** ~Table IV! is only 3.7%.
From the fit we also learn that the greater right-sign ex-cess seen inB1 vs B0Q distributions—while expected fromthe greaterBu
(* ,** ) hadronization excess~see Fig. 9!—is fur-ther exaggerated in Fig. 11 by the additionalB** →Bp6
cross talk, and the asymmetry reduction occurring inB0 me-sons due toB02B0 mixing.
Finally, we find theB** production fraction, i.e., theprobability that ab quark hadronizing into a lightB mesonforms an orbitally excited state, to be
h** 50.2860.06~stat!60.03~syst!. ~8!
The breakdown of these uncertainties is shown in Table VI.The statistical error can be attributed to several sources: theB meson sample size, the component arising from the statis-tical limitations in the constraint of the hadronization shape~the ‘‘floating hadronization’’! to the lD (* ) data, and, simi-larly, from the statistical error in the determination of the‘‘constrained floating’’ fit parameters that are based on thelD (* ) data sample~i.e., PV and the soft pion efficiency!. Thesystematic uncertainty also has three major classes: the con-strained floating parameters of the fit that are determined
8As mentioned before, the the powerR in Eq. ~2! is fixed to 1.1~from the simulation! sinceR is an excess degree of freedom in theparametrization.
FIG. 11. The sideband subtractedB-p6Q distributions of thedata~points! compared to the fit results. The dashed curves are thefitted hadronization component, the dotted histograms include allbackgrounds, and the solid histograms are the totals including thefitted B** signal.
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externally to thelD (* ) sample~i.e., the ‘‘external param-eters’’ listed in the lower portion of Table IV!, the systemat-ics associated with the hadronization asymmetry parametri-zation ~i.e., what is left over after accounting for the abovestatistical uncertainty in its parametrization!, and the contri-bution from gluon splitting. As expected, the largest contri-bution to the statistical uncertainty comes from floating theshape of the hadronization component in the fit. Similarly,the largest contribution to the systematic uncertainty comesfrom varying the nominal hadronization asymmetry. Thisanalysis would thus greatly benefit from a more precisemeans of determining the hadronization background.
To test the hypothesis that background fluctuations couldaccount for our observation, we fit many Monte Carlo gen-eratedQ distributions of background only, randomized torepresent the statistical power of the data sample. We foundthat the probability of such a fluctuation to mimic theB**signal is lower than 1026, including systematic effects.
The experimental resolution does not enable us to disen-tangle the fourB** states, but we may determine an average
mass of the ensemble. We assume the relative productionrates of the four mesons are governed by spin counting anduse a theoretical prediction of the mass splittings. Templatesof the B** Q distributions are constructed for different setsof B** masses. The shape of the distribution is dominatedby the smearing caused by missing daughter particles, pre-dominantely the neutrino, and any separation between thefour states is largely washed out. For a given hypothesis ofthe mass splittings, we fit the expected shape of theB**template to the data while collectively varying the masses bystepping through the mass of the narrowest state, theB1 ~J51, j q5 3
2 !. The x2’s of the fits of the templateQ distribu-tions, derived from the splittings calculated in Ref.@9#, areshown on the left-hand side of Fig. 12 as a function ofm(B1). The minimum corresponds to
m~B1!55.7160.02~stat%syst!GeV/c2, ~9!
TABLE IV. Fit parameters and results for extracting theB** fraction: The four freely floating parameters,which determine theB** fraction and hadronization shapes, are distinguished by their ‘‘input values’’ being‘‘free.’’ The remaining parameters are the constrained floating parameters, which have ax2 term constrainingthem in the fit to the listed ‘‘input value’’ by their ‘‘input error.’’ The constrained parameter above thedividing line contributes to the statistical uncertainty of the final result~as it depends upon the data sample!.Systematic uncertainties arise from those parameters below the line, i.e., the so-called ‘‘external parameters,’’which are determined from sources external to this the data sample. The ‘‘output error’’ column is thereforea combination of statistical and apart of the systematic uncertainties, as discussed in the text.
Fit parametersInputvalue
Inputerror
Outputvalue
Outputerror
B** fraction h** Free ¯ 0.28 0.06B1 hadronization normalization Nu Free ¯ 0.95 0.13B0 hadronization normalization Nd Free ¯ 0.92 0.12Q-hadronization width W Free ¯ 0.23 0.01RelativeD** →D* p rate PV 0.33 0.28 0.42 0.24
Reconstruction efficiency forps eps0.74 0.02 0.86 0.07
Relative rate ofB→n lD * vs n lD Rf 2.5 0.6 2.3 0.6Fraction ofB→ lX decays toD** ’s f ** 0.36 0.12 0.32 0.11Ratio of B1 to B1 lifetimes tB1 /tB0 1.02 0.05 1.03 0.05Ratio of Bs
0 to Bd0 hadronization f s / f d 0.30 0.07 0.29 0.07
Effective x for B0 mixing xeff 0.21 0.01 0.21 0.01Reconstruction efficiency forB from B** eB** 0.763 0.012 0.76 0.01Reconstruction efficiency forp from B** ep** 0.531 0.015 0.53 0.02Reconstruction efficiency forp from D** eD** 0.160 0.009 0.16 0.01Reconstruction efficiency forB from Bs** es** 0.623 0.025 0.62 0.02Reconstruction efficiency forK from Bs** eK** 0.664 0.064 0.67 0.06
TABLE V. The values of the fraction parameters describing the light quark composition of the recon-structedB signatures. For example, 82.1% of thelKp events contain aBu
1 , and 17.9% aBd0.
Signature Kp K3p Kpp Kpps K3pps Kpp0ps
au 0.821 0.826 0.195 0.066 0.072 0.077ad 0.179 0.174 0.805 0.934 0.928 0.923
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which is in very good agreement with the predicted valuem(B1)55.719 GeV/c2. Also shown in Fig. 12 are the corre-sponding values ofh** as a function ofm(B1). There is arelatively small dependence, relative to the uncertainty, ofh** on m(B1) in the immediate neighborhood of the fitminimum.
The quoted uncertainty on the mass includes only the sys-tematic effects accounted for in calculating the productionfraction, but does not include the theoretical uncertainty onthe shape of theB** peak. If, for example, we vary thesplitting between theB0* and theB1 states from the assumed119 MeV/c2 to 1170 MeV/c2 @8#, or to 2109 MeV/c2
@10–12#, while preserving the splittings between two wideand the two narrow states, we observe a shift of220 and120 MeV/c2 in the respectivem(B1) values obtained.
V. SUMMARY
In conclusion, we have observed the production of orbit-ally excitedB** mesons inpp collisions and measured theprobability for the creation of anL51 state among the lightB mesons to be 0.2860.06(stat)60.03(syst). In addition,assuming a model-dependent set of splittings for the fourB** states, we extract the mass of the narrowestB** stateto bem(B1)55.7160.02 GeV/c2.
The main advantage of the method presented in thisanalysis over other methods published to date, is that we userelatively little input from the Monte Carlo calculation topredict the properties of the largest background, theb had-ronization particles. The shape-determining parameters ofthe hadronization component are left free to float in the fitand only the ratio of abundances of right-sign and wrong-
sign particles is input from the Monte Carlo calculation. Themain drawback of this approach is the resulting large statis-tical uncertainty on the measuredB** fraction, since thehighly correlated characteristics of the hadronization compo-nent are being determined from the same data.
This analysis is a further step toward experimentally un-raveling the sources of the tagging power of theB flavor-tagging method used in Refs.@3, 5, 6#, and may aid in theconstruction of betterB flavor taggers. Significant improve-ments in this analysis could be obtained in the future by abetter understanding of the hadronization process in theppenvironment, and distinguishing the narrow from the wideB** resonances. This separation may be possible with thelarge exclusively reconstructedB samples available in thenext Tevatron collider run. Such an effort would be greatlyaided byK-p separation from a particle identification sys-tem.
ACKNOWLEDGMENTS
The authors thank the Fermilab staff and the technicalstaffs of the participating institutions for their vital contribu-tions. We also thank T. Sjo¨strand for his suggestions in tun-ing PYTHIA/JETSET. This work was supported by the U.S.Department of Energy and National Science Foundation, theItalian Istituto Nazionale di Fisica Nucleare, the Ministry ofEducation, Science, Sports and Culture of Japan, the NaturalSciences and Engineering Research Council of Canada, theNational Science Council of the Republic of China, theSwiss National Science Foundation, the A. P. Sloan Founda-tion, the Bundesministerium fuer Bildung und Forschung,Germany, and the Korea Science and Engineering Founda-tion.
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FIG. 12. Thex2 of theQ distribution fit as a function of theB1
mass~the narrowJ51 state! is shown on the left. The correspond-ing B** production fraction is shown on the right. TheB1 mass isused to characterize the the mass of theB** states, where thesplittings between the four states are fixed to the theoretical predic-tion of Ref. @9#.
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! 20.010 10.011Total 20.057 10.054
Systematic uncertaintiesExternal parameters 20.013 10.023Hadronization asymmetry 20.023 10.020
NLO bb production 20.005 10.006
Total 20.027 10.031
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![Observation of B_{c} mesons in pp[over ¯] collisions at sqrt[s]=1.8 TeV](https://img.dokumen.tips/doc/110x75/6349a2b2382c55d53a077ae0/observation-of-bc-mesons-in-ppover-collisions-at-sqrts18-tev.jpg)
