Results are presented from four CDF analyses involving heavy quark production
in proton-antiproton collisions at center of mass energy 1.96 TeV. The shapes
of b-jets are found to be broader than inclusive predictions and broader than
both PYTHIA and HERWIG defaults. A measurement of the production cross section
for psi(2S) is consistent with Run 1 results and with theoretical predictions
associated with parton distribution function energy dependence. The inclusive
b-jet production cross section is also consistent with theoretical predictions
over six orders of magnitude. The b-bbar differential production cross section
is compared to several theoretical models and found to be best described by
MC@NLO + JIMMY.Comment: ICHEP08, 5 figure

Seidel, Sally

English

arXiv

Results are presented from four CDF analyses involving heavy quark production in proton-antiproton collisions at center of mass energy 1.96 TeV. The shapes of b-jets are found to be broader than inclusive predictions and broader than both PYTHIA and HERWIG defaults. A measurement of the production cross section for {psi}(2S) is consistent with Run 1 results and with theoretical predictions associated with parton distribution function energy dependence. The inclusive b-jet production cross section is also consistent with theoretical predictions over six orders of magnitude. The b{bar b} differential production cross section is compared to several theoretical models and found to be best described by MC{at}NLO + JIMMY

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arXiv:0808.3347v1  [hep-ex]  25 Aug 2008Heavy Quark Production at the TevatronSally SeidelDepartment of Physics and Astronomy,University of New Mexico, Albuquerque, NM 87131for the CDF CollaborationResults are presented from four CDF analyses involving heavy quark production in proton-antiproton collisions at center of mass energy 1.96 TeV. The shapes of b-jets are found to be broaderthan inclusive predictions and broader than both PYTHIA and HERWIG defaults. A measurementof the production cross section for ψ(2S) is consistent with Run 1 results and with theoreticalpredictions associated with parton distribution function energy dependence. The inclusive b-jetproduction cross section is also consistent with theoretical predictions over six orders of magnitude.The bb differential production cross section is compared to several theoretical models and found tobe best described by MC@NLO + JIMMY.I. INTRODUCTIONWe report on four measurements by the CDF Experiment [1] of processes involving heavy quark production. Alluse data recorded at center of mass energy 1.96 TeV at the Fermilab Tevatron Collider during Run II.II. MEASUREMENT OF b-JET SHAPES IN INCLUSIVE JET PRODUCTIONThe structure of jets derives from the gluon emissions from the primary parton involved. In heavy quark jets, thequark decay must be modeled as well as the underlying event. Multi-gluon emission is difficult to calculate so isoften approximated by parton shower models. Jet shape is known to depend upon whether the primary parton is aquark or a gluon, and it is also expected to depend upon flavor. It is expected to depend as well upon the productionmechanism; for example, the b and b from gluon splitting are expected to be often in the same jet [2], producing abroader jet than does flavor creation. Measurement of jet shapes casts light on all these aspects of jet evolution andheavy flavor production.To address the question of whether the fraction of b-jets originating from gluon splitting, and its evolution, iswell described by contemporary models, we define the jet shape, a measure of the fraction of total jet transversemomentum pT, inside a given radius in the space of rapidity y and azimuthal angle φ. This is Ψ(r/R) ≡ 〈pT (0→r)pT (0→R)〉,the fraction of total pT in cone R carried by particles in subcone r, averaged over an ensemble of jets, normalized to1, and defined such that Ψ(0) = 0 and particles outside the cone are excluded.The b-jet event selection begins with triggers based solely on calorimeter transverse energy ET. Trigger Level 1requires one calorimetric trigger tower above a threshold between 5 and 10 GeV. Level 2 seeks clusters about theLevel 1 towers among adjacent towers above 1 GeV and requires that at least one cluster exceed a threshold between15 and 90 GeV. Level 3 applies the Run 1 cone algorithm [3] and imposes EminT greater than 20 to 100 GeV. The jetminimum pT requirement is set to ensure that only events for which the trigger is ≥ 99% efficient are used. Oﬄinethe jets are reconstructed by the Midpoint Cone Algorithm [4]. The selection of b-jets is then enhanced by requiringa secondary vertex. Because b’s tend to be found near the jet axis, the search for them uses a cone of radius R = 0.4in (y, φ) space. Tracks are ranked by reconstruction quality, including the contribution from the distance d0 of closestapproach to the primary vertex. The algorithm next attempts to reconstruct a secondary vertex, beginning with thehighest quality track. If this succeeds, a cut is placed on the significance of the two-dimensional projection alongthe jet axis of the distance between the primary and secondary vertices. General event quality cuts follow, includinga rejection of multiple interactions (there must be one and only one primary vertex with |z| < 50 cm), a rejectionof cosmics based on the significance of the missing ET , and a requirement of jet centrality: |yjet| ≤ 0.7. The jetFERMILAB-CONF-08-326-EpT is corrected to the hadron level by matching hadron and calorimeter level jets in Monte Carlo, a correction thatincreases the pT by 20% to 10% with no change in jet shape.The requirement of the secondary vertex tag biases the measured jet shapes by demanding clean, well-definedtracks. An r-dependent correction for this is needed. There are additionally corrections for the presence of non-b jetsmisidentified as b-jets, corrections for detector effects (for example, the number of calorimeter towers scales with pT),and a correction for the presence of a second b quark in the jet. The data are fitted to two-b and one-b templatesseparately. The final function to be fitted is given by Ψbhad = Chad(r/R)·Ψtagdet(r/R)−(1−pb)bnon−b(r/R)Ψnon−bdet(r/R)pbbb(r/R), whereChad is the unfolding factor Ψbhad(r/R)/Ψbdet(r/R), Ψtagdet is the measured jet shape for the tagged sample, Ψnon−bdet isthe measured inclusive jet shape, pb is the purity of b’s in the tagged jet sample, and bb and bnon−b correct for biasesto the jet shape arising from the secondary vertex requirement. The data are compared to predictions by PYTHIA,with Tune A [5], and HERWIG v 6.506 [6]. The principle systematics are associated with the choice of Monte Carlomodel, the effect of the calorimeter model, the jet energy calibration, and assumptions about the c-quark content ofthe jets.The results of the study [7], for integrated luminosity 300 pb−1, are shown in Figure 1, for 4 bins in pT. In each bin,the data are compared to the PYTHIA prediction for inclusive jets as well as the PYTHIA and HERWIG predictionsfor single b production and for single b production with the default fraction diminished by 20%. One sees that thedata are incompatible with the inclusive prediction: the jet shapes are evidently influenced by the presence of heavyquarks, and b-jets are broader. One also sees that the data jets are broader than the PYTHIA and HERWIG defaults;the leading order models underestimate the fraction of b’s from gluon splitting and the fraction of jets with two b’s.III. MEASUREMENT OF THE PRODUCTION CROSS SECTION OF THE ψ(2S)The mechanism for producing heavy vector mesons in hadron collisions is not well understood. CDF Run I dataon production cross sections for prompt J/ψ and ψ(2S) were one to two orders of magnitude above predictions bycolor singlet models. Subsequent theoretical efforts [8] with adjusted production matrix elements match the crosssection but predict increasing transverse polarization with production pT that is not confirmed by the data [9]. Newapproaches [10, 11] have been proposed. The ψ(2S) is a good testing ground for studying charmonium hadropro-duction as there are no significant charmonium states above it to produce feeddown. The goal of this study is ameasurement of σ(pp→ ψ(2S)) · BR(ψ(2S)→ µ+µ−) for 2 ≤ pT ≤ 30 GeV/c.The data selection begins with muons reconstructed in four layers of the central tracking chamber and matched tothree to four hit tracks in the muon detector. Events that pass the dimuon trigger, which requires two opposite signtracks, each with significant pT, are required to have three hits in the silicon vertex detector SVX II. The ψ(2S) massand lifetime are fit with a lifetime function, and requirements are placed on the dimuon mass, 3.5 < m(µµ) < 3.8GeV/c2, and rapidity |y(µµ)| < 0.6.CDF separates the signal from background, and the prompt from the b-decay ψ’s, with an unbinned maximumlikelihood fit in candidate mass and proper decay length ct. The mass separates the signal from the background. Thesignal is modeled with the Crystal Ball Function [12], a Gaussian core with a low side tail. The mass background ismodeled with a first order polynomial. The prompt signal is separated from the feeddown with a ct-fit. The promptsignal is given by a double Gaussian centered on zero. The long-lived signal is modeled by an exponential convolutedwith a Gaussian. The lifetime background is modeled by a prompt double Gaussian plus symmetric, positive-ct, andnegative-ct long-lived components. The likelihood function is given by L = fsPmasss (fpPctp + (1 − fp)PctE⊗G) + (1 −fs)Pmassbkg (fsymPctsym + f+Pct+ + f−Pct− + (1 − fsym − f+ − f−)Pctp ), where the f ’s are fractions of signal (s, from thetotal number of candidates in the fit), prompt (p), symmetric long-lived background (sym), positive-ct long-livedbackground (+), and negative-ct long-lived background(-). The P ’s are probability density functions for signal mass(Pmasss ), linear mass background (Pmassbkg ), prompt signal double Gaussian proper time (Pctp ), an exponential convolvedwith a Gaussian for b-decay signal (P ctE⊗G), and lifetime backgrounds (Pctsym, Pct+ , and Pct− ).The efficiency calculation is given by the product of six terms whose values range from 95.3% to 99.9%. The0.20.40.60.81 80 GeV/c≤ T52 < p(r/R) bΨ=0.75mergeMidPoint R=0.7, f 0.7≤|jet|Y 104 GeV/c≤ T80 < pCDF II preliminary0.2 0.4 0.6 0.8 100.20.40.60.81 142 GeV/c≤ T104 < p0.2 0.4 0.6 0.8 1dataPythia Tune A:b-0.21bb finclHerwig:b-0.21bb f 300 GeV/c≤ T142 < pr/RFIG. 1: The measured integrated b-jet shapes for four pT bins. The data are shown as open squares where the error barsrepresent the statistical and total uncertainties. The statistical uncertainties are smaller than the squares. The data arecompared to PYTHIA Tune A (solid lines) and HERWIG (dashed lines). The uppermost solid curve is the inclusive prediction;the next solid curve, and the uppermost dashed curve, are the predictions with the default f1b fraction; and the lowest solidcurve and lowest dashed curve are the predictions with the default 1b fraction diminished by 20%.acceptance calculation is complicated by the fact that acceptance depends upon polarization per pT bin, yet CDFpolarization data on the ψ(2S) are too weak for direct application. The J/ψ polarization, for which strong CDFdata exist, are, however, expected to correlate highly with prompt ψ(2S) polarization, so after confirming that theJ/ψ and ψ(2S) polarization data are consistent, CDF applies the J/ψ polarization values to the ψ(2S) pT bins.Monte Carlo ψ(2S) samples are generated with fixed polarizations at the extreme values of 0 and -1 and with flatdistributions in pT, η, and φ. These samples are simulated in the CDF detector and reconstructed. We compute theproduct of geometrical acceptance and trigger efficiency, A = Nrec(pT)×(Neff (pT)/Nrec(pT))Ngen(pT), where for Ngen generatedevents, N rec survive geometric and reconstruction requirements and N eff survive the trigger. A ranges from 0.0053to 0.2548. We interpolate the data to intermediate polarization values predicted from the J/ψ data. The principlesystematic uncertainties on this measurement are associated with the luminosity, the reconstruction efficiency, thedimuon trigger efficiency, and the ψ(2S) polarization. The variation of the prescale during the course of collectingintegrated luminosity 1.1 fb−1 produces an effective integrated luminosity of 954 pb−1.The resulting prompt ψ(2S) differential cross section is shown in Figure 2. One sees that in all three cases, the RunI result is confirmed with an order of magnitude more statistics. The measured value of σ(pp→ ψ(2S))·BR(ψ(2S)→(2S)) [GeV/c]ψ(Tp0 5 10 15 20 25 30*BR [nb/(GeV/c)]T/dPσd-510-410-310-210-1101-1(2S): Run II Nominal 1.1 fbψPrompt )-1                       (Actual 954 pb>)T                   (stat.+syst. at <p-1(2S): Run I 18 pbψPrompt                 (stat.+syst. at bin center)-1CDF II Preliminary 1.1 fbFIG. 2: The prompt production cross section versus pT for data from CDF Run I (triangles) and Run II (circles).µ+µ−) is 0.68± 0.01± 0.06 nb. The ratio of the Run II to the Run I result, for identical ranges in pT, is 18± 19%.The theoretical prediction [13] for this ratio, including the energy dependence of the parton distribution functions,is 14± 8%.IV. STUDY OF INCLUSIVE b-JET PRODUCTIONMeasurements of b quark production in hadronic collisions test perturbative QCD. The CDF Run I inclusiveB meson cross section measurement [14] motivated theoretical developments beyond next-to-leading order [15].Continued comparisons, at higher pT and with increased statistics, may motivate further improvements.This study considers events whose primary vertex has |z| < 50 cm, whose missing ET is not significant, and whosekinematical variables lie in the range 38 < pjetT < 400 GeV/c and |yjet| < 0.7, with jets reconstructed with theMidpoint Cone Algorithm and heavy flavor jets tagged via their secondary vertices. The jet energy corrections arebased on minimum bias events which measure the pT deposited in the calorimeter, as a function of the number ofprimary vertices, and indicate a value of 0.93 ± 0.14 GeV/c per extra vertex. Monte Carlo events from PYTHIA6.203, with Tune A and the CTEQ5L parton distribution function set, are used to correct the measured energy foreffects of partially instrumented regions and calorimeter nonlinearities. Typical unfolding factors range from 1.6 to2.1. The b quark content of the jet is inferred from the shape of the invariant mass of all charged tracks attached to]2Mass secondary vertex [GeV/c0 1 2 3 4 5 6N tagged jets (Data)020040060080010001200 0.029± = 0.318 bBin 82-90 GeV/c: fData (Jet50)Fit prediction tagged jets × bf tagged jets × non-bfCDF RunII PreliminaryFIG. 3: The measured secondary vertex mass distribution for jets with corrected jet pT in the range 80 to 92 GeV/c, comparedto the result from the fit to Monte Carlo templates for b and non-b jets.the secondary vertex, as shown in Figure 3. The measurement is compared to the theoretical prediction described in[16].The measured differential cross section,d2σb−jetdpTdy=Ntaggedfbǫb−tag∆yjet∆pjetT∫Ldt, is shown in Figure 4 for integrated lumi-nosity 300 pb−1. Here Ntagged is the number of tagged jets in each pT bin, ∆pT is the bin size, fb is the fraction of jetsin the tagged sample (this ranges from 0.35 at low pT to 0.14 at high), ǫb−tag is the b-tagging efficiency, ∆yjet is thejet rapidity range, and L is the luminosity. The measured cross section is consistent with the theoretical predictionthroughout the full six orders of magnitude of range in pT. It exhibits a strong dependence on scale µ, however,which suggests that higher orders may make large contributions. The largest systematic uncertainties derive fromthe luminosity, the jet energy scale, the jet energy resolution, the unfolding process, the b-tagging efficiency, and thefraction of b-jets, and produce a total systematic uncertainty that ranges from ±25% at low pT to ±70% at high pT.V. STUDY OF THE PRODUCTION OF bb DIJETSMomentum conservation requires that the azimuthal angle φ between a b and b produced at lowest order mustbe 180◦. Higher order QCD processes produce additional partons in the final state, modifying the range of allowedazimuthal angle difference, ∆φ. Order α3s diagrams are thought to contribute the same magnitude to the cross sectionas order α2s diagrams. Measuring the cross section as a function of ∆φ provides information on the contributions ofthe leading order and next-to-leading order terms.The event selection requires two central calorimeter towers with significant ET in association with two tracks in thecentral tracking chamber with significant pT. The calorimeter towers are clustered, and the tracks are reconstructedwith the Silicon Vertex Trigger [17]. Events having two clusters with significant ET associated with two trackshaving significant displaced vertices are retained. Jets are reconstructed with the Run I cone algorithm. One ormore high-quality primary vertices are required. Corrections are applied to the jet energy scale as well as to theenergies of b-jets (whose fragmentation, for example, is harder than that of light quarks). The presence of two jets jet [GeV/c]TP50 100 150 200 250 300 350 400 (nb/[GeV/c])T/dYdPσ2 d10-710-610-510-410-310-210-1110DataSystematic errorsNLO prediction CTEQ6Mcorrected at hadron level / 2b2+mT2P=Fµ=RµNLO uncertainties )0µ < µ / 4 < 0µ(scale included =0.75 merge=0.7, fconeMidPoint jets, R-1 L ~ 300 pb∫ = 1.96 TeV, s|Y|<0.7CDF RunII PreliminaryFIG. 4: The measured inclusive b-jet cross section (filled circles) as a function of pjet compared with the next-to-leading orderperturbative QCD prediction (empty crosses). The shaded band represents the systematic uncertainty on the data and thedashed band represents the uncertainty on the theory.with significant ET, both b-tagged and with displaced secondary vertices, is confirmed. The data are compared topredictions by PYTHIA, with Tune A; HERWIG; and MC@NLO [18] with the HERWIG parton shower and theunderlying event generated by Jimmy 4.3 [19]. The systematics are dominated by the jet energy scale and rangefrom 20 to 30%.For integrated luminosity 260 pb−1, all three Monte Carlos show similar agreement with data distibutions of bbproduction cross section versus leading jet ET and versus dijet invariant mass. The cross section as a function of ∆φ,however, is significantly better modeled by MC@NLO, as shown in Figure 5. The peak at large angles reflects flavorcreation, and the excess at small angles is due to higher order diagrams and multiple interactions. The measuredtotal cross section for |η12| < 1.2, ET1 > 35 GeV, and ET2 > 32 GeV is σ = 5664± 168± 1270 pb.[1] D. Acosta et al., Phys. Rev. D 71, 032001 (2005).[2] S. Frixione et al., hep-ph/9702287.[3] F. Abe et al., Phys. Rev. D 45, 1448 (1992).[4] G.C. Blazey et al., hep-ex/0005012; D. Acosta et al., Phys. Rev. D 74, 071103(R), 2006.[5] T. Sjo¨strand et al., Comp. Phys. Comm. 135, 238 (2001); R. Field and R. Group, arXiv: hep-ph/0510198.[6] G. Corcella et al., JHEP 01, (2001) 010.[7] A. Abulencia et al., arXiv:0806.1699 [hep-ex], 2008.[8] G.T. Bodwin, E. Braaten, and G.P. Lepage, Phys. Rev. D 51, 1125 (1995); E. Braaten and S. Fleming, Phys. Rev. Lett.74, 3 327 (1995).[9] A. Abulencia et al., Phys. Rev. Lett. 99, 132001 (2007).[10] S.P. Baranov, Phys. Rev. D 66, 114003 (2002).[11] V.A. Khoze et al., Eur. Phys. J. C 39, 163 (2005).[12] J. Gaiser, SLAC-0255 (1982).[13] K. Anikeev et al., hep-ph/0201071 (2001).[14] F. Abe et al., Phys. Rev. Lett. 75, 1451 (1995).[15] M. Cacciari and P. Nason, Phys. Rev. Lett. 89, 122003-1 (2002). (rad)φ ∆0 0.5 1 1.5 2 2.5 3) [pb/rad]φ ∆ d(η/dσ2 d210310Data - Syst. uncertaintyPythia (CTEQ5L) Tune AHerwig (CTEQ5L) + JimmyMC@NLO (CTEQ6M) + Jimmy-1 = 1.96 TeV, L~260 pbs|<1.2η=0.4, |coneJetClu R>32 GeVT,2>35 GeV, ET,1ECDF Run II PreliminaryFIG. 5: The bb jet cross section as a function of the dijet ∆φ correlation. Data are compared to hadron level cross sectionsobtained using MC@NLO+JIMMY, PYTHIA, and HERWIG+JIMMY. The shaded area represents the total systematicuncertainty on the data.[16] S. Frixione and M. Mangano, Nucl. Phys. B 483, 321 (1997).[17] A. Bardi et al., Nucl. Instr. and Meth. A 485, 178 (2002).[18] S. Frixione and B. Webber, JHEP 0206 (2002) 029.[19] J.M. Butterworth, J.R. Forshaw, M.H. Seymour, Z. Phys. C 72, 637 (1996).

Heavy Quark Production at the Tevatron

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