EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2012-124 2013/01/28 CMS-BPH-11-007 Λ Λ Λ Measurement of the cross section and the to ratio b √ b b with J/ψΛ decays in pp collisions at s = 7TeV 3 1 The CMS Collaboration∗ 0 2 n a J 5 2 ] Abstract x e - p TheΛ differentialproductioncrosssectionandthecross-sectionratioσ(Λ )/σ(Λ ) e b b b [h aremeas√uredasfunctionsoftransversemomentum pTΛb andrapidity|yΛb|inppcolli- sionsat s = 7TeVusingdatacollectedbytheCMSexperimentattheLHC.Themea- 2 surementsarebasedonΛ decaysreconstructedintheexclusivefinalstateJ/ψΛ,with b v thesubsequentdecaysJ/ψ → µ+µ− andΛ → pπ,usingadatasamplecorresponding 4 9 to an integrated luminosity of 1.9fb−1. The product σ(Λ )×B(Λ → J/ψΛ) versus b b 5 pΛb fallsfasterthanthatofbmesons. Themeasuredvalueofσ(Λ )×B(Λ → J/ψΛ) 0 T b b 5. for pTΛb > 10GeV and |yΛb| < 2.0 is 1.16±0.06±0.12 nb, and the integrated 0 σ(Λ )/σ(Λ ) ratio is 1.02±0.07±0.09, where the uncertainties are statistical and b b 2 systematic,respectively. 1 : v i X SubmittedtoPhysicsLettersB r a ∗SeeAppendixAforthelistofcollaborationmembers 1 1 Introduction Crosssectionsforb-quarkproductioninhigh-energyhadroniccollisionshavebeenmeasured at pp colliders at center-of-mass energies from 630GeV [1] to 1.96TeV [2–4], in fixed-target p- nucleus collisions with beam energies from 800 to 920GeV [5], and recently in pp collisions at 7TeV at the Large Hadron Collider (LHC) [6–13]. As the expected cross sections can be calculated in perturbative quantum chromodynamics (QCD), the comparison between data andpredictionsprovidesacriticaltestofnext-to-leading-order(NLO)calculations[14,15]. Considerable progress has been achieved in understanding heavy-quark production at Teva- tronenergies,largelyresolvingearlierdiscrepanciesinwhichtheoreticalpredictionsweresig- nificantly below observed production rates [15]. However, substantial theoretical uncertain- ties on production cross sections remain due to the dependence on the renormalization and factorization scales. Measurements of b-hadron production at 7TeV represent a test of the- oretical approaches that aim to describe heavy-flavor production at the new center-of-mass energy [16, 17]. Furthermore, understanding the production rates for b hadrons represents an essential component in accurately estimating heavy-quark backgrounds for various searches, suchasH0 → bbandsupersymmetricorexoticnewphysicssignatureswithbquarks. Λ This Letter presents the first measurement of the production cross section of a b baryon, , √ b fromfullyreconstructedJ/ψΛdecaysinppcollisionsat s = 7TeVandcomplementsthemea- surementsofB+[6],B0[7],andB0[9]productioncrosssectionsalsoperformedbytheCompact s MuonSolenoid(CMS)experimentattheLHC[18]. Thecomparisonofbaryonproductionrela- tivetomesonproductionresultingfromthesameinitialb-quarkmomentumspectrumallows for tests of differences in the hadronization process. Such differences are particularly interest- ing in the context of heavy-baryon production in relativistic heavy-ion collisions, where the medium could significantly enhance the production of heavy baryons relative to mesons [19– 21]. Furthermore,theppinitialstateattheLHCallowstestsofbaryontransportmodels,which predictrapidity-dependentantibaryon/baryonasymmetries,incontrasttobaryon-antibaryon Λ Λ pairproduction,whichtypicallyresultsinequalyields[22,23]. Measurementsofthe to b b cross-section ratio, σ(Λb)/σ(Λb), as f√unctions of pTΛb and |yΛb| allow for the first test of such modelswithheavy-quarkbaryonsat s = 7TeV. Events with Λ baryons reconstructed from their decays to the final state J/ψΛ, with J/ψ → b µ+µ− and Λ → pπ, are used to measure the differential cross sections dσ/dpΛb ×B(Λ → T b J/ψΛ),dσ/dyΛb×B(Λb → J/ψΛ),andσ(Λb)/σ(Λb)withrespecttothetransversemomentum pΛb and the rapidity |yΛb|, as well as the integrated cross section times branching fraction for T pΛb > 10GeVand|yΛb|< 2.0. Thecrosssectiontimesbranchingfractionisreportedinsteadof T thecrosssectionitselfbecauseofthe54%uncertaintyonB(Λ → J/ψΛ)[24]. Thecrosssection b timesbranchingfractionmeasurementsareaveragedoverparticleandantiparticlestates,while theratioiscomputedbydistinguishingthetwostatesviadecaystoporp,respectively. 2 Detector The data sample used in this analysis was collected by the CMS experiment in 2011 and cor- responds to an integrated luminosity of 1.86±0.04fb−1 [25]. A detailed description of the detectormaybefoundelsewhere[18]. Themaindetectorcomponentsusedinthisanalysisare thesilicontrackerandthemuondetectionsystems. The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5, where η = −ln[tan(θ/2)] and θ is the polar angle of the track relative to the counterclock- 2 3 Eventselection wise beam direction. It consists of 1440 silicon pixel and 15148 silicon strip detector modules andislocatedinthe3.8Tfieldofthesuperconductingsolenoid. Itprovidesanimpactparam- eter resolution of about 15µm and a p resolution of about 1.5% for particles with transverse T momentaupto100GeV. Muonsaremeasuredinthepseudorapidityrange|η| < 2.4,withde- tectionplanesmadeusingthreetechnologies: drifttubes,cathodestripchambers,andresistive plate chambers. Events are recorded with a two-level trigger system. The first level is com- posed of custom hardware processors and uses information from the calorimeters and muon systems to select the most interesting events. The high-level trigger processor farm further decreasestheeventratefromabout100kHztoaround350Hzbeforedatastorage. 3 Event selection Earlydatatakingconditionsin2011utilizedaloosedimuontriggerwiththefollowingrequire- ments. Events are selected requiring two oppositely charged muons with dimuon transverse momentum greater than 6.9GeV. Displaced muon pairs from long-lived b-hadron decays are preferentiallyselectedbyfurtherrequiringatransverseseparationfromthemeanppcollision position(”beamspot”)greaterthanthreetimesitsuncertainty, wheretheuncertaintyincorpo- rates the vertex and beamspot measurements. Also required at the trigger level are a dimuon vertex fit confidence level larger than 0.5% and cosα > 0.9, where α is defined as the angle in the plane transverse to the beams between the dimuon momentum and the vector from the beamspot to the dimuon vertex. The dimuon invariant mass mµ+µ− is required to satisfy 2.9 < mµ+µ− < 3.3GeV. Forthelater46%ofthedataset,thetriggerwastightenedbyincreasing thedimuonvertexfitconfidencelevelthresholdto10%andimposingkinematicrequirements of pµ > 3.5GeVand|ηµ| < 2.2foreachofthemuons. Theremaining2011datawererecorded T witheventightertriggersandarenotusedintheanalysis. Muoncandidatesarefullyreconstructedbycombininginformationfromthesilicontracker[26] and muon detectors, and are required to be within the kinematic acceptance region of pµ > T 3.5GeV and |ηµ| < 2.2. Muon candidates are further required to have a track χ2 per degree of freedom <1.8, at least 11 silicon tracker hits, at least two hits in the pixel system, and to be matched to at least one track segment in the muon system. Multiple muon candidates are not allowedtosharethesamemuontracksegments[27]. Opposite-signmuonpairsarefittoacommonvertextoformJ/ψcandidates,whicharerequired tobewithin150MeVoftheworld-averageJ/ψmass[24]. TheJ/ψcandidatesarealsorequired to have p greater than 7GeV, a dimuon vertex fit confidence level larger than 0.5%, cosα > T 0.95, and a transverse separation of the vertex from the beamspot greater than three times its uncertainty. Λ The candidates are formed by fitting oppositely charged tracks to a common vertex. Each track is required to have at least 6 hits in the silicon tracker, a χ2 per degree of freedom <5, and a transverse impact parameter with respect to the beamspot greater than 0.5 times its un- certainty. Theprotoncandidate, identifiedasthehigher-momentumtrack, isrequiredtohave p > 1.0GeV. Misassignment of the correct proton track is found to be negligible from sim- T ulation. The reconstructed Λ decay vertex must have a χ2 per degree of freedom <7 and a transverseseparationfromthebeamspotatleastfivetimeslargerthanitsuncertainty. Thein- variantmassm isrequiredtobewithin8MeVoftheworld-averageΛmass[24]. Candidates pπ arerejectedifmπ+π− iswithin20MeVoftheworld-averageK0S mass[24]. Λ Λ The candidates are formed by combining a J/ψ candidate with a candidate. A vertex- b Λ constrained fit is performed with the two muons and the candidate, with the invariant 3 Λ Λ masses of the J/ψ and candidates constrained to their world-average values [24]. The b Λ vertex fit confidence level is required to be greater than 1% and the reconstructed mass b must satisfy 5.2 < mJ/ψΛ < 6.0GeV. Multiple Λb candidates are found in less than 1% of the events with at least one candidate passing all selection criteria. In those cases, only the can- didate with the highest Λb vertex fit confidence level is retained. The mJ/ψΛ distributions for Λ Λ selected and candidatesareshowninFig.1. b b ) ) 450 V 500 CMS V CMS e e G s = 7 TeV G 400 s = 7 TeV 02 400 L = 1.9 fb-1 02 350 L = 1.9 fb-1 0. L only 0. L only b 300 b ( ( / / 300 s s 250 t t n n e e v v 200 E 200 E 150 100 100 50 0 0 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.3 5.4 5.5 5.6 5.7 5.8 5.9 m (GeV) m (GeV) J/Y L J/Y L Figure1: FitresultsforthemJ/ψΛ distributionforΛb (left)andΛb (right)for pTΛb > 10GeVand |yΛb| < 2.0,wherethedashedlineshowsthebackgroundfitfunction,thesolidlineshowsthe sumofsignalandbackground,andthepointsindicatethedata. 4 Efficiency determination Λ The efficiency for triggering on and reconstructing baryons is computed with a combina- b tion of techniques using the data and large samples of fully simulated Monte Carlo (MC) sig- nal events generated with PYTHIA 6.422 [28], decayed by EVTGEN [29], and simulated using GEANT4 [30]. Theefficiencyisfactorizedaccordingto (cid:101) = A·(cid:101)µ1 ·(cid:101)µ2 ·(cid:101)µ1 ·(cid:101)µ2 ·(cid:101)µµ ·(cid:101)Λb, (1) trig trig reco reco trig sel where each term is described below. The trigger ((cid:101)µi ) and muon-reconstruction efficiencies trig ((cid:101)µi ) are obtained from a large sample of inclusive J/ψ → µ+µ− decays in data using a ”tag- reco and-probe”techniquesimilartothatdescribedinRef.[31],whereonemuonisidentifiedwith stringentqualityrequirementsandthesecondmuonisidentifiedusinginformationeitherex- clusively from the tracker (to measure the trigger and offline muon-identification efficiencies) or from the muon system (to measure the trigger and offline tracking efficiencies). While, in principle, the inclusive J/ψ → µ+µ− sample can include signal events, which could bias the measurement, in practice the fraction is negligibly small and provides an unbiased measure- mentofthemuonefficiencies. For the portion of the trigger efficiency that depends on single-muon requirements ((cid:101)µi ), the trig Λ efficiency for a given event is computed as the product of the two single-muon efficien- b cies. However, the trigger efficiencies for dimuon events where the muons bend toward each 4 5 Fittingprocedure other are up to 30% lower than for events where the muons bend away from each other for certainportionsofthedetector. Thisinefficiencyariseswhenthemuontrajectoriescrossinthe muon system, and one of the candidates is rejected because of shared hits. To account for this effect, the trigger efficiencies for muons that bend toward and away from each other are com- putedseparatelyindataandtheappropriateefficiencyisappliedtoeachclassofsignalevents. This procedure naturally accounts for the correlations between the two single-muon efficien- cies,asconfirmedinsimulation. Theportionsofthetriggerefficiencythatdependondimuon µµ quantities((cid:101) )aremeasuredfromaninclusiveJ/ψsamplecollectedwithtriggerswhereonly trig single-muonrequirementsareapplied. Theprobabilitiesforthemuonstoliewithinthedimuonkinematicacceptanceregion(A)and for the Λ and Λ candidates to pass the selection requirements ((cid:101)Λb) are determined from b b sel the simulated events. To minimize the effect of the PYTHIA modeling of the pΛb and |yΛb| T distributionsontheacceptanceandefficiencycalculations,thesimulatedeventsarereweighted to match the kinematic distributions observed in the data. The simulated events used for the efficiency calculations have also been reweighted to match the measured distribution of the number of pp interactions per event (pileup). On average, there are six pileup interactions in Λ thedatasampleusedinthisanalysis. Theefficienciesforhadrontrackreconstruction[32], b reconstruction [33], and fulfilling the vertex quality requirements are found to be consistent betweendataandsimulation. The total efficiency of this selection, defined as the fraction of Λ → J/ψΛ with J/ψ → µ+µ− b andΛ → pπdecaysproducedwithpΛb > 10GeVand|yΛb| < 2.0thatpassallcriteria,is0.73%. T Λ Λ The efficiency ranges from 0.3% for p b 10–13GeV to 4.0% for p b > 28GeV, with the largest T T Λ losses due to the reconstruction (10–16% efficiency), the dimuon kinematic acceptance (12– Λ 63%),andthedisplaceddimuontriggerrequirements(33–56%). Theefficienciesinbinsof p b T and|yΛb|areshowninTable1. To measure the ratio of antiparticle to particle cross sections σ(Λ )/σ(Λ ), only the ratio of b b Λ Λ the and detection efficiencies is needed. Many of the efficiency contributions cancel in b b the ratio, including all the J/ψ and µ efficiencies since the particle and antiparticle states are Λ Λ indistinguishable. However,the and reconstructionefficienciesdifferbecauseofdifferent interaction cross sections with the detector material; the p are more likely to suffer a nuclear Λ interaction and be lost, resulting in an efficiency that is on average 13% lower for than for b Λ Λ Λ , as shown in Table 2. The ratio of the and selection efficiencies is calculated from b b b simulationasdescribedaboveforthecombinedsample,wherethesimulationmodelingofthe detectorinteractionsisvalidatedbycomparingthenumberofhitsreconstructedontrackswith that observed in data. The uncertainty on the amount of detector material and the appropri- ateness of simulated interaction cross sections are considered as systematic uncertainties, as describedinSection7. 5 Fitting procedure The backgrounds are dominated by nonprompt J/ψ production from b hadrons. The dimuon invariant-mass distribution in data confirms that the contamination from events containing a misidentifiedJ/ψisnegligibleafterallselectioncriteriahavebeenapplied. Backgroundevents aredistinguishedfromsignalbytheirreconstructedmJ/ψΛ distribution,whichisfoundtobein goodagreementbetweendataawayfromthesignalpeakandsimulatedb → J/ψXevents. The Λ proper decay length distribution in data confirms that the background events arise from b long-lived b hadrons, and therefore offers no additional discriminating power between signal 5 andbackground. Themeasuredm distributionshowsapurityof77%genuineΛeventsafter pπ applyingthefullselectioncriteria,whilethemπ+π− distributionconfirmsthatmorethan99.9% oftheK0 backgroundisrejectedbythekaonmass-windowveto. S The Λb yields are extracted from unbinned extended maximum-likelihood fits to the mJ/ψΛ distribution in bins of pΛb and |yΛb| defined in Table 1. In each bin, the signal is described T by a double-Gaussian function with resolution parameters fixed to values found when fitting simulated signal events and means set to a common value left free in the fit. The background shape is modeled with a third-order polynomial, whose parameters are left free to float inde- pendentlyineachbin. Theratioofantiparticletoparticleyieldsisobtainedbysimultaneously Λ Λ fitting the and mass distributions, with resolution parameters fixed from the fit to the b b Λ Λ combined and simulated sample and common mean allowed to float. The background b b shapes are fit with separate third-order polynomials, whose parameters are left free in the fit. The signal mass resolution varies as a function of |yΛb|, ranging from a mean of 11MeV for Λ Λ central to27MeVforforward events. b b 6 Results Thefittedsignalyieldsineachbinof pΛb and|yΛb|aresummarizedinTable1. Figure1shows T thefitstothemJ/ψΛ distributionsforΛb andΛb candidatesintheinclusivesamplewith pTΛb > 10GeV and |yΛb| < 2.0. The total number of signal events extracted from an inclusive fit is 1252±42,wheretheuncertaintyisstatisticalonly. TheΛ differentialcrosssectiontimesbranchingfractioniscalculatedinbinsof pΛb as b T dσ(pp → ΛbX) ×B(Λ → J/ψΛ) = nsig , (2) dpΛb b 2·(cid:101)·B·L·∆pΛb T T and similarly for |yΛb|, where nsig is the fitted number of signal events in the given bin, (cid:101) is the average efficiency for signal Λ and Λ baryons to pass all the selection criteria, L is b b the integrated luminosity, ∆pΛb is the bin size, and B is the product of branching fractions T B(J/ψ → µ+µ−) = (5.93±0.06)×10−2 and B(Λ → pπ) = 0.639±0.005[24]. Theadditional Λ factor of two in the denominator accounts for our choice of quoting the cross section for b productiononly,whilen includesbothΛ andΛ . Theefficienciesarecalculatedseparately sig b b for each bin, always considering only baryons produced with |yΛb| < 2.0 for pΛb bins and T pΛb > 10GeV for |yΛb| bins, and taking into account bin-to-bin migrations (0–2%) because of T thefiniteresolutiononthemeasured pTΛb and|yΛb|. EqualproductionofΛbandΛbisassumed fortheefficiency,aspredictedbyPYTHIAandasisconsistentwithourmeasurement. The measured differential cross sections times branching fraction versus pΛb and |yΛb| are T shown in Fig. 2 and Table 1. They are compared to predictions from the NLO MC generator POWHEG 1.0 with the hvq package [34, 35] using a b-quark mass mb = 4.75GeV, renormaliza- (cid:113) tion and factorization scales µ = m2 +p2, CTEQ6M parton distribution functions [36], and b T PYTHIA 6.422 [28] for the parton hadronization. The uncertainty on the predicted cross sec- tioniscalculatedbyvaryingtherenormalizationandfactorizationscalesbyfactorsoftwoand, independently, m by ±0.25GeV. The largest variation in each direction is taken as the uncer- b tainty. The data are also compared to the PYTHIA 6.422 prediction, using a b-quark mass of 4.80GeV, CTEQ6L1 parton distribution functions, and the Z2 tune [37] to simulate the under- lyingevent. NoattempthasbeenmadetoquantifytheuncertaintyonthePYTHIApredictions. 6 6 Results Table 1: Λ + Λ signal yield n , efficiency (cid:101), and measured differential cross sections times b b sig branching fraction dσ/dpTΛb ×B(Λb → J/ψΛ) and dσ/dyΛb ×B(Λb → J/ψΛ), compared to the POWHEG [34, 35] and PYTHIA [28] predictions. The uncertainties on the signal yields are statisticalonly,whilethoseontheefficienciesaresystematic. Theuncertaintiesinthemeasured cross sections are statistical and systematic, respectively, excluding the common luminosity (2.2%)andbranchingfraction(1.3%)uncertainties. The POWHEG and PYTHIA predictionsalso haveuncertaintiesof54%duetoB(Λ → J/ψΛ),whicharenotshown. b pTΛb nsig (cid:101) dσ/dpTΛb ×B(Λb → J/ψΛ) POWHEG PYTHIA (GeV) events (%) (pb/GeV) (pb/GeV) (pb/GeV) 10−13 293±22 0.29±0.03 240±20±30 110+40 210 −30 13−15 240±18 0.79±0.08 108±8±12 54+21 102 −12 15−18 265±19 1.54±0.16 41±3±4 29+10 55 −6 18−22 207±16 2.34±0.23 15.6±1.2±1.6 13.4+4.5 24.0 −2.7 22−28 145±14 3.21±0.34 5.3±0.5±0.6 5.3+1.6 9.3 −1.1 28−50 87±11 3.96±0.50 0.70±0.09±0.09 0.89+0.32 1.42 −0.15 |yΛb| nsig (cid:101) dσ/dyΛb ×B(Λb → J/ψΛ) POWHEG PYTHIA events (%) (pb) (pb) (pb) 0.0−0.3 233±17 0.74±0.09 370±30±50 180+70 330 −40 0.3−0.6 256±18 0.77±0.09 390±30±50 170+60 330 −40 0.6−0.9 206±16 0.81±0.09 300±20±30 170+60 320 −40 0.9−1.2 196±17 0.70±0.08 330±30±40 160+60 300 −40 1.2−1.5 189±17 0.67±0.09 330±30±50 150+50 280 −40 1.5−2.0 162±18 0.65±0.09 180±20±30 130+50 250 −30 The measured pT spectrum falls faster than predicted by POWHEG and PYTHIA, while the |y| spectrum shape is in agreement with the predictions within uncertainties, as illustrated in the data-to-POWHEG ratio plots shown in the lower panels of Fig. 2. The integrated cross section σ(pp → ΛbX)×B(Λb → J/ψΛ) for pTΛb > 10GeV and |yΛb| < 2.0, calculated as the sum over all p bins, is 1.16±0.06±0.12 nb, where the first uncertainty is statistical, and the sec- T Λ ondissystematic. Forthetotalcrosssectionresult, thehighest p b binisfitwithoutanupper T bound and has a yield of 97.0±13.2 events. The total cross section measurement is in good agreement with the prediction from PYTHIA of 1.19±0.64nb and higher than the prediction from POWHEG of 0.63+0.41nb, where the uncertainties are dominated by the 54% uncertainty −0.37 onB(Λ → J/ψΛ)[24]. b This result can be compared to previous CMS measurements of B+ [6], B0 [7], and B0 [9] pro- √ s duction at s = 7TeV. To facilitate the comparison, the B+ and B0 results are taken for the range pBT > 10GeV. Simulated events are generated with MC@NLO [38] with mb = 4.75GeV and CTEQ6M parton distribution functions to determine the fraction of B+, B0, and B0 events s within the pB and |yB| ranges used for their respective measurements with the p > 10GeV T T and |y| < 2.0 requirements used in this analysis. Scaling by the appropriate ratio and using theworld-averagevaluesof B(Λ → J/ψΛ) = (5.7±3.1)×10−4 and B(B0 → J/ψφ) = (1.4± b s 0.5)×10−3 [24], we determine the following cross sections for pB > 10GeV and |yB| < 2.0: T σ(pp → B+X) = 6.7±1.0µb; σ(pp → B0X) = 6.7±0.8µb; σ(pp → B0X) = 2.5±1.0µb s and σ(pp → Λ X) = 2.1±1.1µb, where the uncertainties are the quadrature sum of the b 7 V) b) nb/Ge 10-1 Ls = LC= 1 M7.9 ST febV-1 X) (n LLs = C= 1 M7.9 ST febV-1 X) ( |y b| < 2.0 LYJ/ 0.4 pTb > 10 GeV Data L PYTHIA fiX YJ/ POWHEG b POWHEG uncertainty 10-2 L fiX b fipp L dy( 0.2 fip / p ( sd T p d 10-3 Data / PYTHIA sd POWHEG POWHEG uncertainty EG 2.510 20 30 40 L 50 EG 2.50 0.5 1 1.5 L 2 H 2 p b (GeV) H 2 |y b| W 1.5 T W 1.5 O 1 O 1 P P ata/ 10 20 30 40pL b (GeV5)0 ata/ 0 0.5 1 1.5 |yL b2| d T d Λ Figure 2: Upper: Measured differential cross sections times branching fraction dσ/dp b × T B(Λb → J/ψΛ)(left)anddσ/dyΛb×B(Λb → J/ψΛ)(right)comparedtothetheoreticalpredic- tionsfromPYTHIAandPOWHEG. Theinnererrorbarscorrespondtothestatisticaluncertainties andtheouteronesrepresenttheuncorrelatedsystematicuncertaintiesaddedinquadratureto the statistical uncertainties. The dashed lines show the uncertainties on the POWHEG predic- tions. Overall uncertainties of 2.2% for the luminosity and 1.3% for the J/ψ → µ+µ− and Λ → pπ branching fractions for the data are not shown, nor is the 54% uncertainty due to B(Λb → J/ψΛ) for the PYTHIA and POWHEG predictions. Lower: The ratio of the measured valuestothe POWHEG predictions. Theerrorbarsincludethestatisticalanduncorrelatedsys- tematicuncertaintiesonthedataandtheshape-onlyuncertaintiesonthePOWHEGpredictions. statistical and systematic components. No uncertainty has been included for the phase-space extrapolationbasedonMC@NLO[38]. Thelargesystematicuncertaintiesforσ(pp → B0X)and s σ(pp → Λ X) are dominated by the poorly known branching fractions B(Λ → J/ψΛ) and b b B(B0 → J/ψφ),respectively. Theratiosamongthefourresultsareingoodagreementwiththe s world-averageb-quarkfragmentationresults[24]. Theworld-averageb-quarkfragmentationresultsassumethatthefractions arethesameforb jetsoriginatingfromZdecaysatLEPanddirectlyfromppcollisionsattheTevatron. However, measurementsof fΛ performedatLEP[39,40]andattheTevatron[41]showdiscrepancies. A b recentresult[42]fromtheLHCbCollaborationmeasuresastrong p dependenceoftheratioof T Λb productiontoB-mesonproduction, fΛb/(fu+ fd),with fΛb ≡ B(b → Λb)and fq ≡ B(b → Bq). Larger fΛ valuesareobservedatlower pT,whichsuggeststhatthediscrepancyobserved b betweentheLEPandTevatrondatamaybeduetothelower p oftheΛ baryonsproducedat T b theTevatron. AcomparisonofthisandpreviousCMSresultsforb-hadronproductionversus p isshownin T theleftplotofFig.3,wherethedataarefittotheTsallisfunction[43],  (cid:113) −n p2 +m2−m 1 dN T = CpT1+  . (3) N dp nT T Here C is a normalization parameter, T and n are shape parameters, m is the mass of the b hadronand N istheb-hadronyield. Thestatisticalandbin-to-binsystematicuncertaintiesare 8 6 Results used in the fits. The T parameter represents the inverse slope parameter of an exponential, which dominates at low p . Since our data do not constrain that region well, T is fixed to the T mean value found from fitting the B+ and B0 distributions, where the p threshold is lowest. T The result of T = 1.10GeV is used to obtain the following values of the n parameter, which controls the power-law behavior at high p : n(B+) = 5.5±0.3, n(B0) = 5.8±0.3, n(B0) = T s 6.6±0.4, and n(Λ ) = 7.6±0.4. The larger n value for Λ indicates a more steeply falling p b b T Λ distributionthanobservedforthemesons,alsosuggestingthattheproductionof baryons, b relative to B mesons, varies as a function of p , with a larger Λ /B ratio at lower transverse T b momentum. The right plot of Fig. 3 shows the pΛb spectrum shape compared to B+ and B0, T wherethedistributionsarenormalizedtothecommonbinwith p =10−13 GeV. T ) 10 ) V CMS s = 7 TeV B+ (|yB+| < 2.4) V) CMS s = 7 TeV e G B+ Tsallis fit e b/ B0 (|yB0| < 2.2) G mX) ( 1 BBB0s00 (TT|ssyaaBlls0|ll ii<ss 2ffii.tt4) 10-13 1 dron 10-1 LL sbb (T|syaL lbl|i s< f2i.t0) (dpT10-1 a / h sd b- 10-2 )/( T p fip d 10-2 B+ (|yB+| < 2.4) (p / B0 (|yB0| < 2.2) dpT10-3 s(d L b (|yL b| < 2.0) / sd 10 20 30 40 50 10 20 30 40 50 b-hadron p (GeV) b-hadron p (GeV) T T Figure 3: Comparison of production rates for B+ [6], B0 [7], B0 [9], and Λ versus p . The left s b T plotshowstheabsolutecomparison,wheretheinnererrorbarscorrespondtothetotalbin-to- bin uncertainties, while the outer error bars represent the total bin-to-bin and normalization uncertainties added in quadrature. Fits to the Tsallis function [43] for each distribution are also shown.The overall uncertainties for B0 and Λ are dominated by large uncertainties on s b B(B0 → J/ψφ)andB(Λ → J/ψΛ),respectively. Therightplotshowsashape-onlycomparison s b wherethedataarenormalizedtothe10−13 GeVbinin p andtheerrorbarsshowthebin-to- T binuncertaintiesonly. B0isomittedbecausethe10−13 GeVbinisnotavailableforthecommon s normalization. Theratioσ(Λb)/σ(Λb)iscalculatedinbinsof pTΛb or|yΛb|as Λ n b (cid:101)(Λ ) σ(Λ )/σ(Λ ) = sig × b , (4) b b nΛb (cid:101)(Λ ) sig b wherenΛb andnΛb aretheantiparticleandparticleyieldsinagivenbin,and(cid:101)(Λ )and(cid:101)(Λ ) sig sig b b are the particle and antiparticle efficiencies for a given bin, always considering only baryons producedwith|yΛb| < 2.0for pΛb binsand pΛb > 10GeVfor|yΛb|bins. Theresultsversus pΛb T T T and|yΛb|areshowninFig.4andTable2. Theratioσ(Λb)/σ(Λb)isfoundtobeconsistentwith unity and constant as a function of both pΛb and |yΛb|, within the uncertainties, as predicted T by POWHEG and PYTHIA. Therefore, no evidence of increased baryon production at forward