Article
Reference
Measurement of the B
+production cross section in pp collisions at s√=1960 GeV
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We present a new measurement of the B+ meson differential cross section dσ/dpT at s√=1960 GeV. The data correspond to an integrated luminosity of 739 pb−1 collected with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider. B+ candidates are reconstructed through the decay B+→J/ψK+, with J/ψ→μ+μ−. The integrated cross section for producing B+ mesons with pT≥6 GeV/c and |y|≤1 is measured to be 2.78±0.24 μb.
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the B
+production cross section in pp collisions at s√=1960 GeV. Physical Review. D , 2007, vol. 75, no. 01, p.
012010
DOI : 10.1103/PhysRevD.75.012010
Available at:
http://archive-ouverte.unige.ch/unige:38430
Disclaimer: layout of this document may differ from the published version.
Measurement of the B
production cross section in p p collisions at p s
1960 GeV
A. Abulencia,24J. Adelman,13T. Affolder,10T. Akimoto,56M. G. Albrow,17D. Ambrose,17S. Amerio,44D. Amidei,35 A. Anastassov,53K. Anikeev,17A. Annovi,19J. Antos,14M. Aoki,56G. Apollinari,17J.-F. Arguin,34T. Arisawa,58 A. Artikov,15W. Ashmanskas,17A. Attal,8F. Azfar,43P. Azzi-Bacchetta,44P. Azzurri,47N. Bacchetta,44W. Badgett,17 A. Barbaro-Galtieri,29V. E. Barnes,49B. A. Barnett,25S. Baroiant,7V. Bartsch,31G. Bauer,33F. Bedeschi,47S. Behari,25
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S. Cabrera,16,oM. Campanelli,20M. Campbell,35F. Canelli,17A. Canepa,49S. Carillo,18,iD. Carlsmith,60R. Carosi,47 M. Casarsa,55A. Castro,5P. Catastini,47D. Cauz,55M. Cavalli-Sforza,3A. Cerri,29L. Cerrito,43,mS. H. Chang,28 Y. C. Chen,1M. Chertok,7G. Chiarelli,47G. Chlachidze,15F. Chlebana,17I. Cho,28K. Cho,28D. Chokheli,15J. P. Chou,22 G. Choudalakis,33S. H. Chuang,60K. Chung,12W. H. Chung,60Y. S. Chung,50M. Ciljak,47C. I. Ciobanu,24M. A. Ciocci,47 A. Clark,20D. Clark,6M. Coca,16G. Compostella,44M. E. Convery,51J. Conway,7B. Cooper,36K. Copic,35M. Cordelli,19 G. Cortiana,44F. Crescioli,47C. Cuenca Almenar,7J. Cuevas,11,lR. Culbertson,17J. C. Cully,35D. Cyr,60S. DaRonco,44 M. Datta,17S. D’Auria,21T. Davies,21M. D’Onofrio,3D. Dagenhart,6P. de Barbaro,50S. De Cecco,52A. Deisher,29
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R. Kephart,17U. Kerzel,26V. Khotilovich,54B. Kilminster,40D. H. Kim,28H. S. Kim,28J. E. Kim,28M. J. Kim,12 S. B. Kim,28S. H. Kim,56Y. K. Kim,13N. Kimura,56L. Kirsch,6S. Klimenko,18M. Klute,33B. Knuteson,33B. R. Ko,16
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F. Ptohos,19,eG. Punzi,47J. Pursley,25J. Rademacker,43,bA. Rahaman,48N. Ranjan,49S. Rappoccio,22B. Reisert,17 V. Rekovic,38P. Renton,43M. Rescigno,52S. Richter,26F. Rimondi,5L. Ristori,47A. Robson,21T. Rodrigo,11E. Rogers,24 S. Rolli,57R. Roser,17M. Rossi,55R. Rossin,18A. Ruiz,11J. Russ,12V. Rusu,13H. Saarikko,23S. Sabik,34A. Safonov,54 W. K. Sakumoto,50G. Salamanna,52O. Salto´,3D. Saltzberg,8C. Sa´nchez,3L. Santi,55S. Sarkar,52L. Sartori,47K. Sato,17
P. Savard,34A. Savoy-Navarro,45T. Scheidle,26P. Schlabach,17E. E. Schmidt,17M. P. Schmidt,61M. Schmitt,39 T. Schwarz,7L. Scodellaro,11A. L. Scott,10A. Scribano,47F. Scuri,47A. Sedov,49S. Seidel,38Y. Seiya,42A. Semenov,15
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J. Spalding,17F. Spinella,47T. Spreitzer,34P. Squillacioti,47M. Stanitzki,61A. Staveris-Polykalas,47R. St. Denis,21 B. Stelzer,8O. Stelzer-Chilton,43D. Stentz,39J. Strologas,38D. Stuart,10J. S. Suh,28A. Sukhanov,18H. Sun,57T. Suzuki,56
A. Taffard,24R. Takashima,41Y. Takeuchi,56K. Takikawa,56M. Tanaka,2R. Tanaka,41M. Tecchio,35P. K. Teng,1 K. Terashi,51J. Thom,17,dA. S. Thompson,21E. Thomson,46P. Tipton,61V. Tiwari,12S. Tkaczyk,17D. Toback,54 S. Tokar,14K. Tollefson,36T. Tomura,56D. Tonelli,47S. Torre,19D. Torretta,17S. Tourneur,45W. Trischuk,34R. Tsuchiya,58
S. Tsuno,41N. Turini,47F. Ukegawa,56T. Unverhau,21S. Uozumi,56D. Usynin,46S. Vallecorsa,20N. van Remortel,23 A. Varganov,35E. Vataga,38F. Va´zquez,18,iG. Velev,17G. Veramendi,24V. Veszpremi,49R. Vidal,17I. Vila,11R. Vilar,11
T. Vine,31I. Vollrath,34I. Volobouev,29,nG. Volpi,47F. Wu¨rthwein,9P. Wagner,54R. G. Wagner,2R. L. Wagner,17 J. Wagner,26W. Wagner,26R. Wallny,8S. M. Wang,1A. Warburton,34S. Waschke,21D. Waters,31B. Whitehouse,57
D. Whiteson,46A. B. Wicklund,2E. Wicklund,17G. Williams,34H. H. Williams,46P. Wilson,17B. L. Winer,40 P. Wittich,17,dS. Wolbers,17C. Wolfe,13T. Wright,35X. Wu,20S. M. Wynne,30A. Yagil,17K. Yamamoto,42J. Yamaoka,53
T. Yamashita,41C. Yang,61U. K. Yang,13,jY. C. Yang,28W. M. Yao,29G. P. Yeh,17J. Yoh,17K. Yorita,13T. Yoshida,42 G. B. Yu,50I. Yu,28S. S. Yu,17J. C. Yun,17L. Zanello,52A. Zanetti,55I. Zaw,22X. Zhang,24J. Zhou,53and S. Zucchelli5
(CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, People’s Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798, USA
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254, USA
7University of California, Davis, Davis, California 95616, USA
8University of California, Los Angeles, Los Angeles, California 90024, USA
9University of California, San Diego, La Jolla, California 92093, USA
10University of California, Santa Barbara, Santa Barbara, California 93106, USA
11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
16Duke University, Durham, North Carolina 27708
17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
18University of Florida, Gainesville, Florida 32611, USA
19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
20University of Geneva, CH-1211 Geneva 4, Switzerland
21Glasgow University, Glasgow G12 8QQ, United Kingdom
22Harvard University, Cambridge, Massachusetts 02138, USA
23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
24University of Illinois, Urbana, Illinois 61801, USA
25The Johns Hopkins University, Baltimore, Maryland 21218, USA
26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
28Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea; and SungKyunKwan University, Suwon 440-746, Korea
29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
30University of Liverpool, Liverpool L69 7ZE, United Kingdom
31University College London, London WC1E 6BT, United Kingdom
32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
34Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
35University of Michigan, Ann Arbor, Michigan 48109, USA
36Michigan State University, East Lansing, Michigan 48824, USA
37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
38University of New Mexico, Albuquerque, New Mexico 87131, USA
39Northwestern University, Evanston, Illinois 60208, USA
40The Ohio State University, Columbus, Ohio 43210, USA
41Okayama University, Okayama 700-8530, Japan
42Osaka City University, Osaka 588, Japan
43University of Oxford, Oxford OX1 3RH, United Kingdom
44University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
47Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
49Purdue University, West Lafayette, Indiana 47907, USA
50University of Rochester, Rochester, New York 14627, USA
51The Rockefeller University, New York, New York 10021, USA
52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy
53Rutgers University, Piscataway, New Jersey 08855, USA
54Texas A&M University, College Station, Texas 77843, USA
55Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
56University of Tsukuba, Tsukuba, Ibaraki 305, Japan
57Tufts University, Medford, Massachusetts 02155, USA
58Waseda University, Tokyo 169, Japan
59Wayne State University, Detroit, Michigan 48201, USA
60University of Wisconsin, Madison, Wisconsin 53706, USA
61Yale University, New Haven, Connecticut 06520, USA (Received 10 December 2006; published 29 January 2007) We present a new measurement of theBmeson differential cross sectiond=dpTatps
1960 GeV.
The data correspond to an integrated luminosity of739 pb1collected with the upgraded CDF detector (CDF II) at the Fermilab Tevatron collider.B candidates are reconstructed through the decay B! J= K, withJ= !. The integrated cross section for producingBmesons withpT6 GeV=c andjyj 1is measured to be2:780:24b.
DOI:10.1103/PhysRevD.75.012010 PACS numbers: 13.85.Ni, 12.38.Qk, 13.25.Hw, 14.40.Nd
I. INTRODUCTION
Measurements of the bottom quark production cross section at the Tevatron collider probe the ability of pertur- bative QCD to predict absolute rates in hadronic collisions.
At the perturbative level, calculations of the hard scattering cross sections have been carried out at next-to-leading order (NLO) [1] and also implemented with logarithmic pbT=mb corrections1evaluated to next-to-leading logarith- mic accuracy (NLL) [2]. In both cases, these QCD predic- tions are affected by large theoretical uncertainties such as
aVisiting scientist from University of Athens
oVisiting scientist from IFIC (CSIC-Universitat de Valencia)
nVisiting scientist from Texas Tech University
mVisiting scientist from University of London, Queen Mary and Westfield College
lVisiting scientist from University de Oviedo
kVisiting scientist from Nagasaki Institute of Applied Science
jVisiting scientist from University of Manchester
iVisiting scientist from Universidad Iberoamericana
hVisiting scientist from University of Heidelberg
gVisiting scientist from University of Edinburgh
fVisiting scientist from University of Dublin
eVisiting scientist from University of Cyprus
dVisiting scientist from Cornell University
bVisiting scientist from University of Bristol
cVisiting scientist from University Libre de Bruxelles
1Mass (mb) and transverse momentum (pbT) of the bottom quarks involved in the hard scattering.
MEASUREMENT OF THEB PRODUCTION CROSS. . . PHYSICAL REVIEW D75,012010 (2007)
the dependence on the choice of the renormalization and factorization scales and theb-quark mass [3,4]. Accurate measurements could help in improving the theoretical prediction. Unfortunately, as noted in Ref. [5], measure- ments of theb-quark cross section at the Tevatron appear to be inconsistent among themselves. Reference [5] uses the prediction of a NLO calculation [1] implemented with a nonperturbative model for the b-quark fragmentation2in order to compare all measurements performed at the Tevatron. This calculation predicts pBT 6 GeV=c;jyjB1 0:9b. Previous measurements [9,10] performed by the CDF collaboration at ps
1:8 TeV yield pBT6 GeV=c;jyjB 1 2:660:61and3:60:6b, respectively. The ratios of these measurements to the NLO prediction are (2:90:7) and (4:00:6), respectively. In contrast, the ratios of the CDF and D0 measurements of thebcross section, that are not based upon the detection ofJ= mesons [11–15], to the same theoretical prediction have an appreciably smaller average (2.2 with a 0.2 RMS deviation [5]). The cause of the inconsistency could be experimental difficulties inher- ent to each result or some underlying, and not yet appre- ciated, production of new physics. Therefore, it is of interest to clarify the experimental situation.
This paper presents a new measurement of the B production cross section that uses fully reconstructed B!J= Kdecays. We follow closely the experimental procedure used in Refs. [9,10], but we simplify the analysis selection criteria in order to reduce systematic uncertain- ties. The B production cross section is the ratio of the number of observed B candidates to the product of the detector acceptance, integrated luminosity, and branching fraction of the decayB !J= K withJ= !. We useBcandidates, and theBcross section is derived assuming charge (C) invariance in the production process.
Section II describes the detector systems relevant to this analysis. The data collection, event selection, and B reconstruction are described in Sec. III. In Sec. IV, we evaluate the detector acceptance and derive the total and differential B cross section. Our conclusions are pre- sented in Sec. V.
II. THE CDF II DETECTOR
CDF is a multipurpose detector, equipped with a charged particle spectrometer and a finely segmented calorimeter.
In this section, we describe the detector components that
are relevant to this analysis. The description of these sub- systems can be found in Refs. [16–22]. Two devices inside the 1.4 T solenoid are used for measuring the momentum of charged particles: the silicon vertex detector (SVX II) and the central tracking chamber (COT). The SVX II con- sists of double-sided microstrip sensors arranged in five cylindrical shells with radii between 2.5 and 10.6 cm. The detector is divided into three contiguous five-layer sections along the beam direction for a totalzcoverage3of 90 cm.
The COT is a cylindrical drift chamber containing 96 sense wire layers grouped into eight alternating superlayers of axial and stereo wires. Its active volume coversjzj 155 cm and 40 to 140 cm in radius. The central muon detector (CMU) is located around the central electromagnetic and hadronic calorimeters, which have a thickness of 5.5 inter- action lengths at normal incidence.
The CMU detector covers a nominal pseudorapidity range jj 0:63 relative to the center of the detector, and is segmented into two barrels of 24 modules, each covering 15 in. Every module is further segmented into three submodules, each covering 4.2 inand consisting of four layers of drift chambers. The smallest drift unit, called a stack, covers a 1.2 angle in. Adjacent pairs of stacks are combined together into a tower. A track segment (hits in two out of four layers of a stack) detected in a tower is referred to as a CMU stub. A second set of muon drift chambers (CMP) is located behind an additional steel absorber of 3.3 interaction lengths. Muons which produce a stub in both CMU and CMP systems are called CMUP muons.
The luminosity is measured using gaseous Cherenkov counters (CLC) that monitor the rate of inelasticpp colli- sions. The inelasticppcross section at
ps
1960 GeVis scaled from measurements at
ps
1800 GeV using the calculations in Ref. [23]. The integrated luminosity is determined with a 6% systematic accuracy [24].
CDF uses a three-level trigger system. At Level 1 (L1), data from every beam crossing are stored in a pipeline capable of buffering data from 42 beam crossings. The L1 trigger either rejects events or copies them into one of the four Level 2 (L2) buffers. Events that pass the L1 and L2 selection criteria are sent to the Level 3 (L3) trigger, a cluster of computers running speed-optimized reconstruc- tion code.
For this study, we select events with two muon candi- dates identified by the L1 and L2 triggers. The L1 trigger uses tracks with pT 1:5 GeV=c found by a fast track processor (XFT). The XFT examines COT hits from four
2This calculation uses ab-quark mass ofmb4:75 GeV=c2, renormalization and factorization scales RF
p2Tm2b
q , theMRSD0[6] fit to the parton distribution functions (PDF), and a fragmentation fractionfu0:375. The fragmen- tation model is based on the Peterson fragmentation function [7]
with theparameter set to 0.006 according to fits toee data [8].
3In the CDF coordinate system, and are the polar and azimuthal angles of a track, respectively, defined with respect to the proton beam direction,z. The pseudorapidityis defined as log tan=2. The transverse momentum of a particle ispT Psin. The rapidity is defined asy1=2logEpz=E pz, whereEandpzare the energy and longitudinal momentum of the particle associated with the track.
axial superlayers and provides r information. The XFT finds tracks withpT 1:5 GeV=cin azimuthal sec- tions of 1.25 . The XFT passes the tracks to a set of extrapolation units that determines the CMU towers in which a CMU stub should be found if the track is a muon. If a stub is found, a L1 CMU primitive is generated.
The L1 dimuon trigger requires at least two CMU primi- tives, separated by at least two CMU towers. At L1, there is no requirement that muons have opposite charge. During the data-taking period in which the dimuon sample used for this analysis was collected, the Tevatron luminosity has increased from 1 to 1001030 cm2s1. Accordingly, the L2 trigger, that started with no additional requirement, has incrementally required dimuons with opposite charge, opening azimuthal angle 120 , and single muons with pT 2 GeV=c. All these trigger requirements are mimicked by the detector simulation on a run-by-run basis.
At L3, muons are required to have opposite charge, invari- ant mass in the window 2:7–4:0 GeV=c2, and jz0j 5 cm, where z0 is thez coordinate of the muon track at its point of closest approach to the beam line in ther plane. These requirements define the J= ! trigger.
We use two additional triggers in order to verify the detector simulation. The first trigger (CMUPpT4) selects events with at least one L1 and one L2 CMUP primitive withpT 4 GeV=c, and an additional muon found by the L3 algorithms. Events collected with this trigger are used to measure the muon trigger efficiency. The second trigger (-SVT) requires a L1 CMUP primitive with pT 4 GeV=caccompanied by a L2 requirement of an addi- tional XFT track withpT 2 GeV=cand displaced from the interaction point. These events are used to verify the muon detector acceptance and the muon reconstruction efficiency.
III. DATA SELECTION ANDB RECONSTRUCTION
We search forB!J= Kcandidates in the data set selected by the J= ! trigger. Events are recon- structed offline taking advantage of more refined calibra- tion constants and reconstruction algorithms.
The transverse momentum resolution of tracks recon- structed using COT hits is pT=p2T ’ 0:0017GeV=c1. COT tracks are extrapolated into the SVX II detector and refitted adding hits consistent with the track extrapolation. Stubs reconstructed in the CMU de- tector are matched to tracks withpT 1:3 GeV=c. A track is identified as a CMU muon ifr, the distance in the r plane between the track projected to the CMU chambers and a CMU stub, is less than 30 cm. We also require that muon-candidate stubs correspond to a L1 CMU primitive, and correct the muon momentum for energy losses in the detector.
We search for J= candidates by using pairs of CMU muons with opposite charge, and pT 2 GeV=c (this requirement for each muon track avoids the region of rapidly changing efficiency around the trigger threshold).
The invariant mass of a muon pair is evaluated by con- straining the two muon tracks to originate from a common point in three-dimensional space (vertex constraint) in order to improve the mass resolution. All muon pairs with invariant mass in the range 3:05–3:15 GeV=c2 are considered to beJ= candidates.
If aJ= candidate is found, we search forBmesons by considering all remaining charged particle tracks in the event as possible kaon candidates. As in previous measure- ments [9,10], we select tracks withpT 1:25 GeV=cand withjz0j 1:5 cmwith respect to thez0 position of the J= candidate. We require that kaon-candidate tracks have at least 10 hits in both COT axial and stereo superlayers.
This limits the pseudorapidity acceptance to jj 1:3.
The invariant mass of the K system is evaluated constraining the corresponding tracks to have a common origin while theinvariant mass is constrained to the value of3:0969 GeV=c2[25]. As in Refs. [9,10], we select B candidates with pT 6 GeV=c. From the pseudora- pidity acceptance of CMU muons (jj 0:8) and the pT cuts on theandBtransverse momenta, it follows that:
(i) no kaon fromBdecays is emitted atjj 1:3; (ii) the reconstructedB candidates have rapidityjyj 1.
In contrast with the analyses in Refs. [9,10], we do not require the proper decay length of theBcandidates to be larger than 100m. By doing so, we avoid two large sources of systematic uncertainty: (i) the simulated effi-
2) (GeV/c
µ-
µ+
mK
5.0 5.2 5.4 5.6
)2 candidates/(0.015 GeV/c± B
8000 10000 12000
FIG. 1 (color online). Invariant mass distribution of all B candidates. The line represents a fit to the data using a first order polynomial plus a Gaussian function in order to estimate the background and theBsignal, respectively.
MEASUREMENT OF THEB PRODUCTION CROSS. . . PHYSICAL REVIEW D75,012010 (2007)
ciency of the SVX II detector; (ii) the dependence of the decay length distribution on the simulated SVX II resolu- tion and B transverse momentum distribution. The in- variant mass distribution of allBcandidates found in this study is shown in Fig.1.
IV. DIFFERENTIAL CROSS SECTION To measure the differential cross section, we divide the sample ofBcandidates into fivepTbins: 6 –9, 9 –12, 12 – 15, 15– 25, and25 GeV=c[9,10]. In eachpTbin, we fit the invariant mass distribution of theBcandidates with a binned maximum-likelihood method to determine the number ofBmesons. The fit likelihood uses a Gaussian function to model theBsignal. The background under the B signal arises from combinations ofJ= mesons, 80%
of which do not originate from B decays [26], with random tracks. Combinations ofJ= mesons with a track produced by the sameB-hadron !J= 2 prong de- cay (partially reconstructedB meson) populate the mass region below5:16 GeV=c2. As in previous measurements [9,10], we use a first order polynomial to estimate the underlying combinatorial background (as shown by Fig. 1, the combinatorial background in the mass region above the B meson signal is quite well modeled by a straight line). We fit the data in the invariant mass range 5:18–5:39 GeV=c2. The lower limit is chosen to avoid the region populated by partially reconstructed B-hadron de- cays. The width of the fitted mass range determines the statistical error of the background estimate. Since we have a much larger data set than previous measurements [9,10], we can afford to fit the data in a smaller mass range in order to reduce the systematic uncertainty due to the background modeling.
The average of theBmass values returned by the fits in the differentpTbins is5:2790 GeV=c2with a0:5 MeV=c2 RMS deviation, in agreement with the PDG value [25]. In the fit used to determine the number ofBmesons, we fix theBmass value to5:279 GeV=c2[25]. The width of the Gaussian is a free fit parameter; the value ofreturned by the fit increases from 12:00:4 to 20:00:4 MeV=c2 from the first to lastpT bin, in agreement with the simu- lation prediction. The fits are shown in Figs. 2–6. They return a signal of 2792186, 2373110, 136566, 139063, and27744Bmesons in the fivepT bins.
We have investigated possible systematic uncertainties in the fit results. We have studied the contribution of the B!J= decay mode, the branching fraction of which is 4:90:6%of that of theB!J= Kdecay mode [25].
As shown in Ref. [27], the invariant mass distribution of these Cabibbo-suppressedBdecays, reconstructed assum- ing that pions are kaons, is shifted into the mass region 5:28–5:44 GeV=c2, which partially overlaps with that of the B!J= K decay mode. However, part of this Cabibbo-suppressed contribution is also used by the fit to predict the background under theB!J= K signal with
the effect of reducing its size. When adding the expected contribution of these Cabibbo-suppressed decays, theB! J= Ksignal returned by the fit decreases by11%(we do not apply the 1% correction to the final result, but the uncertainty of the correction is included in the systematic error). We have investigated other possible causes of sys- tematic uncertainties in the B signal estimate. We have
2
) (GeV/c
µ-
µ+
m
K5.0 5.2 5.4 5.6
)
2candidates/(0.015 GeV/c
±B
1500 2000 2500 3000
(GeV/c) < 12 pT
≤ 9
FIG. 3 (color online). Invariant mass distribution ofB can- didates with 9pT12 GeV=c. The line represents the best fit to the data described in the text.
2
) (GeV/c
µ-
µ+
m
K5.0 5.2 5.4 5.6
)
2candidates/(0.015 GeV/c
±B
50005500 6000 6500
7000 6 ≤ pT(GeV/c) < 9
FIG. 2 (color online). Invariant mass distribution ofB can- didates with6pT9 GeV=c. The line represents the best fit to the data described in the text.
compared the results of our fit with those returned using an unbinned likelihood method. We have decreased the fitted mass range to5:24–5:33 GeV=c2, and we have fitted the larger mass interval5:18–5:60 GeV=c2. We have fitted the signal with two Gaussian functions in order to study de- tector resolution effects. TheBsignal returned by these fits does not vary by more than1:5%. Therefore, we attribute an overall2%systematic uncertainty to the fit results.
A. Acceptances and efficiencies
The detector acceptance is calculated with a Monte Carlo simulation based upon a NLO calculation2. The B decay is modeled with theEVTGEN Monte Carlo program [28] that accounts for theJ= longitudinal polar- ization [29]. The detector response to particles produced by Bdecays is modeled with the CDF II detector simulation that in turn is based on the GEANTMonte Carlo program [30]. The simulation includes the generation of L1 CMU trigger primitives. Simulated events are processed and selected with the same analysis code used for the data.
The acceptances estimated using the simulation are listed in TableI. We use the data to verify the detector acceptance and efficiencies evaluated using the CDF II detector simu- lation. We adjust the simulation to match measurements in the data of: (i) the offline COT track reconstruction effi- ciency; (ii) the CMU detector acceptance and efficiency;
µ-
µ+
m
K5.0 5.2 5.4 5.6
)
2candidates/(0.015 GeV/c
±B
500 1000
(GeV/c) < 15 pT
≤ 12
FIG. 4 (color online). Invariant mass distribution ofB can- didates with12pT15 GeV=c. The line represents the best fit to the data described in the text.
TABLE I. Detector acceptance,A, as a function of theBpT. The acceptance Acorr includes corrections evaluated using the data. The average hpTi is the value at which the theoretical differential cross section [1] equals the integrated cross section in each momentum bin divided by the bin width.
pT range (GeV=c) hpTi(GeV=c) A(%) Acorr(%)
6 – 9 7.37 1.545 1:7800:045
9 –12 10.38 3.824 4:4050:111
12 –15 13.39 5.966 6:8720:173
15– 25 19.10 8.819 10:160:25
25 12.516 14:420:36
2
) (GeV/c
µ-
µ+
m
K5.0 5.2 5.4 5.6
)
2candidates/(0.015 GeV/c
±B
200 400 600 800 1000 1200
(GeV/c) < 25 pT
≤ 15
FIG. 5 (color online). Invariant mass distribution ofB can- didates with15pT25 GeV=c. The line represents the best fit to the data described in the text.
2
) (GeV/c
µ-
µ+
m
K5.0 5.2 5.4 5.6
)
2candidates/(0.015 GeV/c
±B
50100 150 200
≥ 25 (GeV/c) pT
FIG. 6 (color online). Invariant mass distribution ofB can- didates withpT 25 GeV=c. The line represents the best fit to the data described in the text.
MEASUREMENT OF THEB PRODUCTION CROSS. . . PHYSICAL REVIEW D75,012010 (2007)
(iii) the efficiency for finding L1 CMU primitives; and (iv) the efficiency of the L1, L2, and L3 triggers.
In the simulation, the offline COT track reconstruction efficiency is given by the fraction of tracks, which at generator level satisfy the pT and selection cuts, that survive after selecting fully simulated events as the data.
The COT track reconstruction efficiency is found to be 0:9980:002. The same efficiency in the data is measured by embedding COT hits generated from simulated tracks intoJ= data. In Ref. [26], the COT track reconstruction efficiency in the data is measured to be 0.996 with a ’ 0:006systematic accuracy.4We conclude that the efficien- cies for reconstructing the K system in the data and the simulation are equal within a 2% systematic error.
Kaon decay and interactions are modeled with the CDF II detector simulation. Because of the uncertainties of the detector materials and the nuclear interaction cross sec- tions, the kaon tracking efficiency has an additional 0.3%
uncertainty [32].
In the simulation, the fraction of CMU stubs generated by muon tracks with pT 2 GeV=c and jj 0:8 is 0:64390:0004. In the data, this efficiency is measured by usingJ= ! decays acquired with the-SVT trigger. We evaluate the invariant mass of all pairs of a CMUP track and a track with displaced impact parameter, pT 2 GeV=c, and jj 0:8. We fit the invariant mass distribution with a first order polynomial plus two Gaussian functions to extract the J= signal. From the number of J= mesons reconstructed using displaced tracks with or without a CMU stub (Fig. 7(a) and 7(b), respectively), we derive an efficiency of0:62510:0047.
The integrated efficiency is evaluated after having weighted the pT and distributions of displaced tracks
in the data to be equal to those of muons fromBdecays in the simulation.
In the simulation, the efficiency for finding a CMU primitive (CMU stub matched by a XFT track) is0:8369 0:0004. This efficiency is measured in the data by using events acquired with the CMUPpT4trigger. We combine the CMUP muon with all other CMU muons found in the event with and without a L1 CMU primitive. We extract the number of J= ! mesons by fitting the invariant mass distributions of all candidates with a first order poly- nomial plus two Gaussian functions. By comparing the fitted numbers of J= candidates with and without L1 CMU primitive (Fig.8(a)and8(b), respectively) we derive an efficiency of0:92760:0005. The integrated efficiency is evaluated after having weighted thepT anddistribu- tions of the additional CMU muons to be equal to that of muons fromBdecays in the simulation.
In the simulation, the efficiencies of the L1 and L2 triggers are 0.9868 and 0.9939, respectively. By studying J= candidates acquired with the CMUPpT4 trigger, the L1 efficiency is measured to be0:98790:0009, and that of the L2 trigger 0:99480:0001. The L3 trigger is not simulated. The L3 trigger efficiency is dominated by dif- ferences between the online and offline reconstruction code efficiency.5The relative L3 efficiency for reconstruct- ing a single muon identified by the offline code has been measured to be 0:9970:002 [26]. The reconstruction efficiencies in the data and in the simulation are summa- rized in Table II.
B. Results
The differential cross sectiond=dpT is calculated as dB
dpT N=2
pTLAcorrBR (1)
2) (GeV/c
µ- µ+
m
3.0 3.1 3.2
)2 candidates / (0.01 GeV/cψJ/
0 5000 10000 15000 20000
ψ (86050+-340) J/
(a)
2) (GeV/c
µ- µ+
m
3.0 3.1 3.2
)2 candidates / (0.01 GeV/cψJ/
0 10000 20000
ψ (51600+-520) J/
(b)
FIG. 7 (color online). Invariant mass distribution of a CMUP muon paired with all charged tracks in the event with (a) or without (b) a CMU stub. Lines represent the fits described in the text.
4The efficiency measurement was performed in a subset of the data used for this analysis. Studies of independent data samples collected in the data-taking period used for this analysis show that changes of the track reconstruction efficiency are appreci- ably smaller than the quoted systematic uncertainty [31].
5Online algorithms are faster but less accurate than the offline reconstruction code.
whereNis the number ofBmesons determined from the likelihood fit to the invariant mass distribution of the J= Kcandidates in eachpTbin. The factor 1/2 accounts for the fact that both B and B mesons are used and assumes C invariance at production. The bin widthpT and Acorr, the geometric and kinematic acceptance that includes trigger and tracking efficiencies measured with the data, are listed in TableI. The integrated luminosity of the data set is L73944 pb1. The branching ratio BR 5:980:22 105is derived from the branching
fractions BRB!J= K 1:0080:035 103 andBRJ= ! 5:930:06 102 [25].
The measuredBdifferential cross section as a function of its transverse momentum is listed in Table III. The integrated cross section is
BpT 6:0 GeV=c;jyj<1 2:780:24b; (2) where the 8.8% error is the sum in quadrature of the 6%
error on the integrated luminosity, the 3.6% uncertainty of theB!J= KandJ= !branching fractions,
2) (GeV/c
µ- µ+
m
3.0 3.1 3.2
)2 candidates / (0.01 GeV/cψJ/
0 50000
100000 (a) (475420+-800) J/ψ
2) (GeV/c
µ- µ+
m
3.0 3.1 3.2
)2 candidates / (0.01 GeV/cψJ/
0 2000 4000 6000
8000 (b) (37130+-230) J/ψ
FIG. 8 (color online). Invariant mass distribution of a CMUP muon paired with all CMU muons in the event with (a) or without (b) a L1 CMU primitive. Lines represent the fits described in the text.
TABLE II. Summary of efficiencies for reconstructingB candidates in the data and the simulation. The last column indicates the corrections applied to the simulated acceptance and used to deriveAcorrin TableI.
Source Data Simulation Corr.
COT tracking 0:9960:0063 0:9980:0023 1:000:02
Kaon interaction 1:0000:003
CMU acc. and eff. 0:62510:00472 0:64390:00042 0:9420:014
L1 CMU primitives 0:92760:00052 0:83690:00042 1:2280:002
L1 eff. 0:98790:0009 0.9868 1:00110:0009
L2 eff. 0:99480:0001 0.9939 1:00090:0001
L3 eff. 0:9970:0022 1 0:9940:004
Total 0:3280:008 0:2830:002 1:1520:029
TABLE III. Observed differential cross section, d=dpT (nb=GeV=c), forB mesons with rapidityjyj 1. Errors are the sum in quadrature of statistical errors (shown in parentheses) and systematic uncertainties due to luminosity (6%), branching ratios (3.6%), acceptance (2.5%), and fitting procedure (2.0%). The relative systematic uncertainties are the same in eachpTbin. The integrated cross section forpT25 GeV=cis21:73:7 nb.
hpTi(GeV=c) Events Acceptance (%) d=dpT
7.38 2792186 1:7800:045 591:759:0(39.3 stat. )
10.38 2373110 4:4050:111 203:217:8(9.4 stat.)
13.39 136566 6:8720:173 74:96:6(3.6 stat.)
19.10 139063 10:160:25 15:51:3(0.7 stat.)
25 27744 14:420:36
MEASUREMENT OF THEB PRODUCTION CROSS. . . PHYSICAL REVIEW D75,012010 (2007)
the 2.5% uncertainty of the acceptance calculation, the 2%
systematic uncertainty of the fit, and the 4.4% statistical error.
For completeness, Fig.9compares transverse momen- tum distributions in the data and in the simulation, based on the NLO QCD prediction2, that has been used to evaluate the detector acceptance. Figure 10 compares B meson rapidity distributions. Data and simulation are normalized to the same number of events. Each distribution is con- structed using J= K candidates with invariant mass in the range 5:255–5:315 GeV=c2 (region #1). The back- ground contribution is subtracted using candidates in the mass range 5.18–5.24 and5:33–5:425 GeV=c2. The back- ground normalization is the number of events in region #1 minus the number ofB candidates determined by the fit listed in TableIII. One notes the fair agreement between data and untuned QCD prediction.6
B±
y
-1.0 -0.5 0.0 0.5 1.0
candidates/(0.02)
±B
0 100 200FIG. 10 (color online). Rapidity distributions ofBmesons in the data () and simulation (solid histogram). The simulation is normalized to theB!Ksignal observed in the data (see text).
(GeV/c)
T B±
p
0 10 20 30
/(1.0 GeV/c) ± number of B
0 200 400 600 800 1000 1200
B±
p
T(GeV/c)
ψ J/
pT
0 10 20 30
/(1.0 GeV/c) ψnumber of J/
0 500 1000 1500
ψ J/
p
T(GeV/c)
µ±
pT
0 5 10 15
/(0.02 GeV/c) ± µnumber of
0 200 400 600 800 1000
1200 µ±
p
T(GeV/c)
K±
pT
0 5 10 15
/(0.02 GeV/c) ± number of K
0 200 400 600 800
K±
p
TFIG. 9 (color online). Transverse momentum distributions in the data () and simulation (solid histogram). The simulation is normalized to theB!Ksignal observed in the data (see text).
6ThepT distributions of theB andJ= mesons in the data are slightly softer than those of the simulation; this difference is not relevant for the result of the study because theBkinematic acceptance has been evaluated for eachpBT bin and the calibra- tion of the simulated acceptance using the data do not depend on the muon and kaon transverse momenta.
