Cross Section for b Jet Production in pbar-p Collisions at sqrt(s) = 1.8 TeV

Cross Section for

b

-Jet Production in

pp

Collisions at

p

p

p

s

5

1

.

8 TeV

B. Abbott,50 _{M. Abolins,}47_{V. Abramov,}23 _{B. S. Acharya,}15 _{D. L. Adams,}57 _{M. Adams,}34_{G. A. Alves,}2_{N. Amos,}46 E. W. Anderson,39M. M. Baarmand,52V. V. Babintsev,23 L. Babukhadia,52 A. Baden,43B. Baldin,33 P. W. Balm,18

S. Banerjee,15 _{J. Bantly,}56 _{E. Barberis,}26 _{P. Baringer,}40_{J. F. Bartlett,}33 _{U. Bassler,}11 _{A. Bean,}40 _{M. Begel,}51 A. Belyaev,22S. B. Beri,13 G. Bernardi,11I. Bertram,24 A. Besson,9V. A. Bezzubov,23 P. C. Bhat,33V. Bhatnagar,13

M. Bhattacharjee,52_{G. Blazey,}35 _{S. Blessing,}31 _{A. Boehnlein,}33 _{N. I. Bojko,}23_{F. Borcherding,}33_{A. Brandt,}57 R. Breedon,27 _{G. Briskin,}56_{R. Brock,}47 _{G. Brooijmans,}33 _{A. Bross,}33 _{D. Buchholz,}36_{M. Buehler,}34_{V. Buescher,}51

V. S. Burtovoi,23 J. M. Butler,44 F. Canelli,51 W. Carvalho,3D. Casey,47 Z. Casilum,52 H. Castilla-Valdez,17 D. Chakraborty,52 _{K. M. Chan,}51 _{S. V. Chekulaev,}23 _{D. K. Cho,}51_{S. Choi,}30 _{S. Chopra,}53 _{J. H. Christenson,}33 M. Chung,34D. Claes,48 A. R. Clark,26 J. Cochran,30L. Coney,38 B. Connolly,31W. E. Cooper,33 D. Coppage,40 M. A. C. Cummings,35 _{D. Cutts,}56_{O. I. Dahl,}26 _{G. A. Davis,}51_{K. Davis,}25 _{K. De,}57_{K. Del Signore,}46 _{M. Demarteau,}33

R. Demina,41P. Demine,9D. Denisov,33 S. P. Denisov,23S. Desai,52 H. T. Diehl,33 M. Diesburg,33 G. Di Loreto,47 S. Doulas,45 _{P. Draper,}57 _{Y. Ducros,}12_{L. V. Dudko,}22_{S. Duensing,}19_{S. R. Dugad,}15 _{A. Dyshkant,}23 _{D. Edmunds,}47

J. Ellison,30 _{V. D. Elvira,}33_{R. Engelmann,}52_{S. Eno,}43 _{G. Eppley,}59_{P. Ermolov,}22 _{O. V. Eroshin,}23 _{J. Estrada,}51 H. Evans,49 V. N. Evdokimov,23T. Fahland,29S. Feher,33 D. Fein,25 T. Ferbel,51H. E. Fisk,33Y. Fisyak,53E. Flattum,33

F. Fleuret,26_{M. Fortner,}35 _{K. C. Frame,}47_{S. Fuess,}33 _{E. Gallas,}33 _{A. N. Galyaev,}23 _{P. Gartung,}30 _{V. Gavrilov,}21 R. J. Genik II,24K. Genser,33C. E. Gerber,34 Y. Gershtein,56 B. Gibbard,53 R. Gilmartin,31 G. Ginther,51B. Gómez,5

G. Gómez,43_{P. I. Goncharov,}23 _{J. L. González Solís,}17 _{H. Gordon,}53_{L. T. Goss,}58_{K. Gounder,}30 _{A. Goussiou,}52 N. Graf,53G. Graham,43P. D. Grannis,52 J. A. Green,39 H. Greenlee,33S. Grinstein,1L. Groer,49P. Grudberg,26 S. Grünendahl,33 _{A. Gupta,}15 _{S. N. Gurzhiev,}23_{G. Gutierrez,}33 _{P. Gutierrez,}55_{N. J. Hadley,}43_{H. Haggerty,}33 S. Hagopian,31 _{V. Hagopian,}31 _{K. S. Hahn,}51_{R. E. Hall,}28_{P. Hanlet,}45 _{S. Hansen,}33 _{J. M. Hauptman,}39 _{C. Hays,}49

C. Hebert,40D. Hedin,35A. P. Heinson,30U. Heintz,44 T. Heuring,31R. Hirosky,34J. D. Hobbs,52B. Hoeneisen,8 J. S. Hoftun,56 _{S. Hou,}46_{Y. Huang,}46 _{A. S. Ito,}33_{S. A. Jerger,}47_{R. Jesik,}37_{K. Johns,}25_{M. Johnson,}33 _{A. Jonckheere,}33 M. Jones,32H. Jöstlein,33A. Juste,33S. Kahn,53E. Kajfasz,10D. Karmanov,22D. Karmgard,38R. Kehoe,38 S. K. Kim,16 B. Klima,33 _{C. Klopfenstein,}27_{B. Knuteson,}26 _{W. Ko,}27 _{J. M. Kohli,}13 _{A. V. Kostritskiy,}23 _{J. Kotcher,}53_{A. V. Kotwal,}49

A. V. Kozelov,23 E. A. Kozlovsky,23J. Krane,39 M. R. Krishnaswamy,15 S. Krzywdzinski,33 M. Kubantsev,41 S. Kuleshov,21 _{Y. Kulik,}52_{S. Kunori,}43_{V. E. Kuznetsov,}30_{G. Landsberg,}56_{A. Leflat,}22_{F. Lehner,}33 _{J. Li,}57 _{Q. Z. Li,}33

J. G. R. Lima,3_{D. Lincoln,}33 _{S. L. Linn,}31_{J. Linnemann,}47 _{R. Lipton,}33 _{A. Lucotte,}52_{L. Lueking,}33 _{C. Lundstedt,}48 A. K. A. Maciel,35R. J. Madaras,26V. Manankov,22H. S. Mao,4T. Marshall,37 M. I. Martin,33R. D. Martin,34 K. M. Mauritz,39_{B. May,}36_{A. A. Mayorov,}37 _{R. McCarthy,}52_{J. McDonald,}31_{T. McMahon,}54_{H. L. Melanson,}33 X. C. Meng,4M. Merkin,22 K. W. Merritt,33C. Miao,56 H. Miettinen,59D. Mihalcea,55 A. Mincer,50 C. S. Mishra,33 N. Mokhov,33 _{N. K. Mondal,}15 _{H. E. Montgomery,}33_{R. W. Moore,}47 _{M. Mostafa,}1_{H. da Motta,}2_{E. Nagy,}10_{F. Nang,}25

M. Narain,44 V. S. Narasimham,15 H. A. Neal,46 J. P. Negret,5S. Negroni,10 D. Norman,58 L. Oesch,46 V. Oguri,3 B. Olivier,11 _{N. Oshima,}33_{P. Padley,}59_{L. J. Pan,}36 _{A. Para,}33 _{N. Parashar,}45_{R. Partridge,}56_{N. Parua,}9_{M. Paterno,}51 A. Patwa,52 _{B. Pawlik,}20 _{J. Perkins,}57 _{M. Peters,}32 _{O. Peters,}18 _{R. Piegaia,}1_{H. Piekarz,}31 _{B. G. Pope,}47_{E. Popkov,}38

H. B. Prosper,31 S. Protopopescu,53 J. Qian,46 P. Z. Quintas,33 R. Raja,33S. Rajagopalan,53 E. Ramberg,33 P. A. Rapidis,33_{N. W. Reay,}41 _{S. Reucroft,}45 _{J. Rha,}30_{M. Rijssenbeek,}52_{T. Rockwell,}47 _{M. Roco,}33 _{P. Rubinov,}33 R. Ruchti,38J. Rutherfoord,25 A. Santoro,2L. Sawyer,42R. D. Schamberger,52 H. Schellman,36A. Schwartzman,1 J. Sculli,50_{N. Sen,}59 _{E. Shabalina,}22_{H. C. Shankar,}15 _{R. K. Shivpuri,}14 _{D. Shpakov,}52_{M. Shupe,}25 _{R. A. Sidwell,}41 V. Simak,7H. Singh,30J. B. Singh,13 V. Sirotenko,33 P. Slattery,51 E. Smith,55 R. P. Smith,33R. Snihur,36 G. R. Snow,48

J. Snow,54 _{S. Snyder,}53 _{J. Solomon,}34 _{V. Sorín,}1_{M. Sosebee,}57_{N. Sotnikova,}22 _{K. Soustruznik,}6_{M. Souza,}2 N. R. Stanton,41 _{G. Steinbrück,}49_{R. W. Stephens,}57_{M. L. Stevenson,}26_{F. Stichelbaut,}53_{D. Stoker,}29 _{V. Stolin,}21

D. A. Stoyanova,23 M. Strauss,55 K. Streets,50M. Strovink,26L. Stutte,33 A. Sznajder,3W. Taylor,52 S. Tentindo-Repond,31_{J. Thompson,}43 _{D. Toback,}43 _{S. M. Tripathi,}27_{T. G. Trippe,}26 _{A. S. Turcot,}53_{P. M. Tuts,}49

P. van Gemmeren,33 V. Vaniev,23 R. Van Kooten,37 N. Varelas,34A. A. Volkov,23A. P. Vorobiev,23 H. D. Wahl,31 H. Wang,36_{Z.-M. Wang,}52_{J. Warchol,}38_{G. Watts,}60_{M. Wayne,}38_{H. Weerts,}47_{A. White,}57_{J. T. White,}58_{D. Whiteson,}26

J. A. Wightman,39D. A. Wijngaarden,19 S. Willis,35 S. J. Wimpenny,30 J. V. D. Wirjawan,58 J. Womersley,33 D. R. Wood,45_{R. Yamada,}33_{P. Yamin,}53_{T. Yasuda,}33_{K. Yip,}33_{S. Youssef,}31_{J. Yu,}33_{Z. Yu,}36_{M. Zanabria,}5_{H. Zheng,}38 Z. Zhou,39_{Z. H. Zhu,}51_{M. Zielinski,}51_{D. Zieminska,}37_{A. Zieminski,}37_{V. Zutshi,}51_{E. G. Zverev,}22_{and A. Zylberstejn}12

(D0 Collaboration)

1_{Universidad de Buenos Aires, Buenos Aires, Argentina} 2_{LAFEX, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, Brazil}

3_{Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil} 4_{Institute of High Energy Physics, Beijing, People’s Republic of China}

5_{Universidad de los Andes, Bogotá, Colombia} 6_{Charles University, Prague, Czech Republic}

7_{Institute of Physics, Academy of Sciences, Prague, Czech Republic} 8_{Universidad San Francisco de Quito, Quito, Ecuador}

9_{Institut des Sciences Nucléaires, IN2P3-CNRS, Universite de Grenoble 1, Grenoble, France} 10_{CPPM, IN2P3-CNRS, Université de la Méditerranée, Marseille, France}

11_{LPNHE, Universités Paris VI and VII, IN2P3-CNRS, Paris, France} 12_{DAPNIA/Service de Physique des Particules, CEA, Saclay, France}

13_{Panjab University, Chandigarh, India} 14_{Delhi University, Delhi, India}

15_{Tata Institute of Fundamental Research, Mumbai, India} 16_{Seoul National University, Seoul, Korea}

17_{CINVESTAV, Mexico City, Mexico}

18_{FOM-Institute NIKHEF and University of Amsterdam/NIKHEF, Amsterdam, The Netherlands} 19_{University of Nijmegen/NIKHEF, Nijmegen, The Netherlands}

20_{Institute of Nuclear Physics, Kraków, Poland}

21_{Institute for Theoretical and Experimental Physics, Moscow, Russia} 22_{Moscow State University, Moscow, Russia}

23_{Institute for High Energy Physics, Protvino, Russia} 24_{Lancaster University, Lancaster, United Kingdom}

25_{University of Arizona, Tucson, Arizona 85721}

26_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720} 27_{University of California, Davis, California 95616}

28_{California State University, Fresno, California 93740} 29_{University of California, Irvine, California 92697} 30_{University of California, Riverside, California 92521} 31_{Florida State University, Tallahassee, Florida 32306}

32_{University of Hawaii, Honolulu, Hawaii 96822} 33_{Fermi National Accelerator Laboratory, Batavia, Illinois 60510}

34_{University of Illinois at Chicago, Chicago, Illinois 60607} 35_{Northern Illinois University, DeKalb, Illinois 60115}

36_{Northwestern University, Evanston, Illinois 60208} 37_{Indiana University, Bloomington, Indiana 47405} 38_{University of Notre Dame, Notre Dame, Indiana 46556}

39_{Iowa State University, Ames, Iowa 50011} 40_{University of Kansas, Lawrence, Kansas 66045} 41_{Kansas State University, Manhattan, Kansas 66506} 42_{Louisiana Tech University, Ruston, Louisiana 71272} 43_{University of Maryland, College Park, Maryland 20742}

44_{Boston University, Boston, Massachusetts 02215} 45_{Northeastern University, Boston, Massachusetts 02115}

46_{University of Michigan, Ann Arbor, Michigan 48109} 47_{Michigan State University, East Lansing, Michigan 48824}

48_{University of Nebraska, Lincoln, Nebraska 68588} 49_{Columbia University, New York, New York 10027} 50_{New York University, New York, New York 10003} 51_{University of Rochester, Rochester, New York 14627} 52_{State University of New York, Stony Brook, New York 11794}

53_{Brookhaven National Laboratory, Upton, New York 11973} 54_{Langston University, Langston, Oklahoma 73050} 55_{University of Oklahoma, Norman, Oklahoma 73019}

56_{Brown University, Providence, Rhode Island 02912} 57_{University of Texas, Arlington, Texas 76019} 58_{Texas A&M University, College Station, Texas 77843}

(Received 15 August 2000)

Bottom-quark production inpp collisions atps苷1.8TeV is studied with 5pb21_{of data collected}

in 1995 by the D0 detector at the Fermilab Tevatron Collider. The differential production cross section forbjets in the central rapidity region (jyb_{j,1) as a function of jet transverse energy is extracted from} a muon-tagged jet sample. Within experimental and theoretical uncertainties, D0 results are found to be higher than, but compatible with, next-to-leading-order QCD predictions.

PACS numbers: 14.65.Fy, 12.38.Qk, 13.85.Qk

Measurements of the bottom-quark production cross section at pp colliders provide an important quantitative test of quantum chromodynamics (QCD). The mass of the b quark is considered large enough (mb ¿ LQCD) to justify perturbative expansions in the strong coupling constant as. Consequently, data on b quark production are expected to be adequately described by calculations at next-to-leading order (NLO) inas [1 – 3].

Past measurements of inclusive b quark production in the central rapidity region, at center-of-mass energies

p

s 苷0.63 TeV [4,5] andps苷1.8TeV [6 – 9], indicate a general agreement in shape with the calculated trans-verse momentum 共pT兲 spectrum, but are systematically higher than the NLO QCD predictions [1 – 3] by roughly a factor of 2.5. More recently, a measurement using muons at high rapidity [10] (2.4,jymj,3.2) to tag

b quarks, indicates an even larger excess of observed cross section over theory. The measured differential production cross section for B mesons [11] is similarly higher than the NLO QCD prediction. Calculations of higher order corrections [12,13] have shown that addi-tional enhancements to the cross section beyond NLO are likely. However, the expected enhancements fall short of accounting for the observed discrepancy between theory and data. This long-standing mismatch has motivated continuous theoretical and experimental effort dedicated to reduce uncertainties in general, and to broaden the scope of observable quantities [9,14].

Previous studies ofb quark production by the D0 Col-laboration have exploited the kinematic relationship be-tweenbquarks and daughter (semileptonic decay) muons to extract integratedbquark production rates as a function ofpTb threshold [7], and have examined azimuthal correla-tions between theb andbin pair production [9].

The present study is a complementary measurement of

b production, based primarily on calorimetry, with the main focus being on b jets rather than b quarks. b jets are defined as hadronic jets carrying b flavor. As op-posed to quarks, jets are directly observable and therefore reduce model dependence when comparing experimental data with theory. This measurement is in direct correspon-dence with a NLO QCD calculation [15] that highlights the advantages of consideringbjets rather than openbquarks. For instance, large logarithms that appear at all orders in the open quark calculation (due to hard collinear gluons) are avoided when all fragmentation modes are integrated.

The differential production cross section ofb jets as a function of the jet transverse energy (ET) has been mea-sured using data collected during 1995 with the D0 detector

at the Fermilab Tevatron Collider. The data correspond to an integrated luminosity of共5.260.3兲pb21_{. The} analy-sis exploits the semileptonic decays ofbhadrons which re-sult in a muon associated with a jet. An inclusive sample of muon-tagged jets is selected from a trigger requiring a jet and a muon, and theb jet component of the inclusive sample is extracted, based on the properties expected of the associated muon and jet.

The D0 detector and trigger system are described else-where [16]. Jet detection utilizes primarily the uranium-liquid argon calorimeters, which have full coverage for pseudorapidity [17]jhj#4, and are segmented into tow-ers ofDh 3 Df 苷0.130.1, wherefis the azimuthal angle. The relative energy resolution for jets is approxi-mately80%兾pE共GeV兲. The central muon system consists of three layers of proportional drift tubes and a mag-netized iron toroid located between the first two layers. The muon detectors provide a measurement of the muon momentum with a resolution parametrized by d共1兾p兲苷

p

关0.18共p 22兲兾p2兴2 ₁共0.003兲2_{, with p in GeV}兾_{c. The} total thickness of the calorimeter and toroid in the central region varies from 13 to 15 interaction lengths, which re-duces the hadronic punchthrough for the muon system to less than 0.5% of muons from all sources.

Initial event selection used a trigger requiring (i)ET . 10GeV in at least one calorimeter trigger tile of Dh 3 Df苷0.831.6, (ii) at least one muon candidate with

pT . 3GeV兾c, and (iii) a singleppinteraction per beam crossing as signaled by the trigger scintillation hodoscopes. Jet candidates were reconstructed off-line with an itera-tive fixed-cone algorithm (cone radius of 0.7 inh-fspace) and then subjected to quality selection criteria to eliminate background from isolated noisy calorimeter cells and ac-celerator beam losses which may mimic jets. Accepted jets were required to haveET .25GeV,jhj,0.6, and an associated muon within the reconstruction cone.

Off-line muon selection required the triggered track to originate from the reconstructed event vertex, withpTm. 6GeV兾candjhm_{j,0.8. Muon candidates in the azimuth} region 80±, fm, 110± were excluded due to poor chamber efficiencies near where the main ring beam pipe passes through D0.

The differentialb jet cross section as a function of jet

ET is extracted from the inclusive tagged jet sample as

ds

dETbJet

苷 U共ET兲Fb共ET兲 2BLintemJ共p

m

T,ET兲A共ET兲

DNmJ

DET

, (1) where DNmJ_兾DE

T represents the inclusive tagged jet counts per transverse energy bin width, Fb共ET兲 is the fraction of tagged jets containing muons from b quark decays,emJ共pmT,ET兲is the event detection efficiency of a

m 1 jet pair,U共ET兲corrects for spectrum smearing from jet energy resolution,A共ET兲corrects for the muon tagging acceptance, Lint is the integrated luminosity of the data sample, andB 苷0.108 60.005is the branching fraction for inclusive decays b !m 1 X [18]. Tagging muons of both charges are counted, and the number of events is divided by 2. The cross section is determined for the 共b 1b¯兲兾2 combination. In Eq. (1) and throughout this paper, ET represents the calorimeter-only component of the jet transverse energy: it excludes the tagging muon and associated neutrino. Once the correction for the lepton energy is included (see below), then ETbJet measures the completeb jet.

The trigger and off-line reconstruction efficiencies were determined from Monte Carlo events, and cross-checked with appropriate control samples of collider data. Monte Carlo events were generated with ISAJET [19], followed by a GEANT[20] simulation of the D0 detector response, trigger simulation, and reconstruction. The overall muon geometric acceptance multiplied by efficiency increases from 35% at pTm苷 6GeV兾c to a plateau of 45% above 10GeV兾c. The overall jet efficiency increases from 85% atET 苷 25GeV to a plateau of 97% above 45 GeV.

The transverse energy of each jet was corrected for the underlying event, additional interactions, noise from ura-nium decay, the fraction of particle energy showered out-side the jet cone, detector uniformity, and detector hadronic response [21]. The steeply falling ET spectrum is dis-torted by jet energy resolution, and was corrected as de-scribed in [22].

In addition tob production, muon-tagged jets can also arise from semileptonic decays of c quarks, and in-flight decays of p or K mesons. Muons from Drell-Yan or on-shellW兾Z boson production are not expected to have associated jets, and Monte Carlo estimates confirm a neg-ligible contribution. The background from light flavors is suppressed using the transverse momentum of the muon relative to the associated jet axis 共pTrel兲 as discriminator. The higher mass of the decayingbquark generates a rather differentpTreldistribution than obtained from quark decays of lighter flavor.

Individual pTrel distributions for muons from b, c (di-rect),c (sequential fromb), andp兾K decays were mod-eled using the ISAJET [19] Monte Carlo, with individual samples of each mode processed through complete detec-tor, trigger, and off-line simulation. Because of the simi-larity of pTrel for c and p兾K sources, within resolution

these distributions were indistinguishable. The b jet sig-nal was extracted on a statistical basis, through maximum likelihood fits to the observedpTrel distribution. The nor-malizations of Monte Carlo templates representing light (c

andp兾K) and heavy (b) quark decay patterns were floated such as to fit the observedpTrel spectra in four ranges of transverse energy. The extracted fraction ofbjets in each

ET range is shown in Fig. 1. The systematic uncertainties were estimated by varying within errors the input distribu-tions to the maximum likelihood fits.

The parametrization of the overall fraction of b jets in the inclusive sample as a function of jet ET was ob-tained from a two-parameter fit (x2 _{苷0.96) to the four} bins inET, and is shown in Fig. 1, together with the un-certainty band (6% relative unun-certainty at 30 GeV, 39% at 100 GeV). The form共a 1 b兾E2T兲was chosen after Monte Carlo fit trials. There are partial bin-to-bin correlations in the uncertainty. The extractedb fraction is the dominant source of uncertainty in the cross section. The upper reach in b jetET is limited by the deteriorating discrimination power ofprelT with increasingET.

Corrections for acceptance loss stem from (i) the tagging threshold for muonpTand range of pseudorapidity, (ii) the muon-jet association (tag) criterion, (iii) the undetected lepton energy of the jet, which is added (statistically) to the hadronicET registered in the calorimeter, and (iv) the restricted pseudorapidity range for jets and muons (theory [15] considersb jets withjhj,1).

The acceptance correction is extracted using theISAJET [19] Monte Carlo simulation, and is defined as the ratio of

bjets satisfying the analysis conditions tobjets satisfying the cross section definition. The transition from ET to

ETbJetis thus included in the correction. The simulatedET andh distributions are in agreement with the data. The overall correction increases from 6% at ET 苷30GeV to 10% at 100 GeV. It is independent of assumed event production rates, and is affected primarily by models for fragmentation and decay. Decays are based on theQQ[23] software package from the CLEO experiment.ISAJETuses the Peterson fragmentation model [24], with a parameter

FIG. 2. Differential cross section forbjet production.

e 苷 0.006that is varied by650%to estimate uncertainty. It is observed that the impact of fragmentation on the ac-ceptance is mainly due to the migration of tagging muons across the minimum-pT boundary. This uncertainty propagates to the cross section as a 9% effect independent of jet ET.

The resultingb jet cross section for jhj,1is shown in Fig. 2, together with the NLO QCD prediction [15]. In-puts to this calculation are the renormalization scale (cho-sen equal to the factorization scale), thebquark pole mass (4.75 GeV兾c2), the parton distribution function (MRSA0 [25]), and the parton clustering algorithm. The uncer-tainty in theory is dominated by the QCD renormalization scale dependence, with the central value in Fig. 2 chosen as m0 苷共ET2 1 Mb兲21兾2, and varied between 2m0 (lower curve) andm0兾2. The fact that there is such a strong depen-dence on scale suggests that important higher-order terms in the calculation are still missing.

The overall systematic uncertainty in the cross section has contributions from the integrated luminosity (5%), trig-ger (3%), and off-line selection (4%) efficiencies, jet ET scale (15%– 8%) and resolution effects (7%– 3%), tagging acceptance (9%–12%), and the extractedbfraction of jets (6%– 39%). Bin-to-bin errors are fully correlated for all sources of uncertainty, except for partial correlations in thebfraction of jets. Cross section values and overall un-certainties, as plotted in Fig. 2, are listed in Table I.

Figure 2 displays the same general pattern of past b

production measurements [4 – 11], with data lying above the central values of the prediction, but comparatively less so in the present case, where general agreement between measurement and the upper band of the theoretical uncer-tainty is observed.

To connect the present measurement with previous find-ings, and in particular the apparent difference in normal-ization with respect to theory, the present data sample (muon-tagged jets) can be reanalyzed from a different per-spective. Instead of focusing on the differentialbjets cross section, the same data can be used to reproduce the inte-gratedbquark cross section as a function of minimumpbT. Similar measurements are described in Refs. [4 – 7] and [9]. The kinematic relationship between daughter muons

TABLE I. Differential cross section forbjet production.

ETbJet ds兾dETbJet Uncertainties (%)

(GeV) (nb兾GeV) Stat. Syst.

27.3 14.4 1.2 20.6

32.3 6.57 1.6 20.1

37.4 3.22 2.1 21.2

42.4 1.65 2.7 23.2

47.4 0.932 3.4 25.6

52.4 0.530 4.2 28.0

57.4 0.292 5.4 30.2

64.7 0.174 4.6 33.2

74.7 0.0678 6.8 36.6

84.7 0.0364 8.7 39.3

94.6 0.0176 11.7 41.5

(pTmspectrum) and parentbquarks (pTb spectrum) is used to extract thebquark production cross section, integrated frompminT to infinity, and over the rapidity rangejybj, 1. HerepTminis defined as the allowedpbTthreshold for a given

pmT distribution. Since thebquark signal fraction increases with muonpT (decreases with jetET),btagging based on

prelT as a function ofp m

T is more precise than as a function of jetET. The model dependence, introduced in the con-version of the muonpTspectrum to the integratedbquark spectrum, dominates the uncertainty in this measurement. The results of this reanalysis are shown in Fig. 3 (trian-gles) along with the theoretical expectation [1] and the pre-vious D0 [9] results. Consistency among all measurements is evident. The present analysis extends significantly the

pbTreach of the previous measurements. This is due to the requirement of jets in the trigger and off-line selection, as opposed to requiring just muon triggers. The jet require-ment naturally forces the sample into a higher region of

pbT. Figure 3 shows that the agreement between data and theory improves somewhat at higherpTb.

In conclusion, two distinct measurements of b quark production in a previously unexplored region of larger transverse momenta have been presented, and are found to be compatible with the NLO QCD calculation for

heavy-flavor production. Agreement between data and theory, unsatisfactory for previous measurements, is now observed to improve at higher transverse momenta.

We thank the staffs at Fermilab and at collaborating institutions for contributions to this work, and acknowl-edge support from the Department of Energy and National Science Foundation (U.S.A.), Commissariat à L’Energie Atomique and CNRS /Institut National de Physique Nu-cléaire et de Physique des Particules (France), Ministry for Science and Technology and Ministry for Atomic En-ergy (Russia), CAPES and CNPq (Brazil), Departments of Atomic Energy and Science and Education (India), Col-ciencias (Colombia), CONACyT (Mexico), Ministry of Education and KOSEF (Korea), CONICET and UBACyT (Argentina), A. P. Sloan Foundation, and the A. von Hum-boldt Foundation.

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