Since the beginning of Run II at the Fermilab Tevatron, the QCD physics groups of the CDF and D0 Collaborations have worked to reach unprecendented levels of precision for many QCD observables. This note summarizes important recent measurements with dataset corresponding to up to 8 fb−1 of total integrated luminosity

Moed Sher, S.

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DOI 10.1393/ncc/i2012-11360-0Colloquia: LaThuile12IL NUOVO CIMENTO Vol. 35 C, N. 6 Novembre-Dicembre 2012Recent QCD studies at the TevatronS. Moed SherFermilab - Batavia, IL, USAricevuto il 7 Settembre 2012Summary. — Since the beginning of Run II at the Fermilab Tevatron, the QCDphysics groups of the CDF and D0 Collaborations have worked to reach unprecen-dented levels of precision for many QCD observables. This note summarizes im-portant recent measurements with dataset corresponding to up to 8 fb−1 of totalintegrated luminosity.PACS 12.38.-t – Quantum chromodynamics.1. – IntroductionThe Tevatron collider at Fermilab provides collisions of protons with anti-protons at acenter-of-mass evergy of 1.96TeV. By the end of the Tevatron Run II, the multipurposedetectors of the CDF [1] and D0 [2] experiments were delivered a total integrated lumi-nosity of about 12 fb−1. This large amount of data is exploit in order to make importantprogress in constraining and confirming the calculations of quantum chromodymanics(QCD) theory. Precise measurements of QCD observables in hadron-hadron collisions,such as jet cross sections, constrain parton density functions (PDFs) and confirms thepredictive power of theory. This results in a better control of the standard QCD pro-duction calculations, which are used to predict major backgrounds for many importantphysical processes. In addition, the specific QCD processes which pose challanges to NewPhysics searches such a supersymmetry and Higgs production can be measured directlywith the increased size of available datasets.In this note some of the recent measurements from the CDF and D0 Collaborationsare reviewed. These measurements are related to QCD hard scattering processes. Abrief introduction to the structure of hadronic collisions is useful as a motivation forjet definition. Hadronic collision may be factorized into perturbative components (hardscattering and initial and final state radiation) and non-perturbative components (beamremnants and multiple parton interactions). These components are illustrated in fig. 1.This simple picture is an example of processes which are modeled by Monte Carlogenerating programs to simulate hadronic collisions. The picture becomes more compli-cated when the properties of QCD color confinement and detector effects are included.c© Societa` Italiana di Fisica 141142 S. MOED SHERFig. 1. – Simple model for hadronic collisions.The colored partons must hadronize into color neutral hadrons. These particles are thenclustered into jets by jets algorithms. Jets may be clustered at the parton (quarks andgluons), particle (hadrons) or detector (calorimeter towers) level. Measurements aremade at the detector level, but it is useful to use the parton and particle level jets fromMonte Carlo simulations to derive corrections to the measured quantities.The analyses discussed in this note focus on the perturbative component of the colli-sion and do not include studies of the non-perturbative regime (where pQCD fails), suchas the “soft” interactions generating the underlying event which accompanies the “hard”collision.2. – Angular decorrelatoins in γ + 2(3) jetsThe D0 Collaboration used inclusive γ+2 jets and γ+3 jets events with an integratedluminosity of about 1 fb−1 to measure cross sections as a function of the angle in theplane transverse to the beam direction between the transverse momentum (PT ) of theγ + leading jet system (jets are ordered in PT ) and the PT of the other jet for the γ + 2jet events, or PT sum of the two other jets for the γ +3 jet events, [3]. Differential crosssections were studies in three bins of the second jet PT . The results are compared todifferent Multiple Particle Intercation (MPI) models and demonstrate that the predictionof the Single Particle (SP) models do not describe the measurements, and an additionalcontribution from Double Parton (DP) events is required to describe the data. Thedata favors the predictions of the new PYTHIA MPI models with PT -ordered showers,implemented in the Perugia and and S0 tunes, and also SHERPA with its default MPImodel. Predictions from previous PYTHIA MPI models with tunes A and DW aredisfavored. The results of these measurements are shown in fig. 2.3. – Three jet mass cross sectionUsing about 0.7 fb−1 of integrated luminosity collected by the D0 experiment, dif-ferential cross sections for three jet mass were measured, [4]. In this measurement jetsare defined by the midpoint cone algorithm with cone size R = 0.7. Five scenarios wereconsidered, where the rapidities of the three leading PT jets are restricted to |y| < 0.8,|y| < 1.6, |y| < 2.4. The transverse momentum selection required PT1 > 150GeV/c, andRECENT QCD STUDIES AT THE TEVATRON 1430 0.5 1 1.5 2 2.5 3SΔ/d3jγσ) d3jγσ(1/-1101               -1 = 1.0 fb intDØ, LDataPYTHIA, tune APYTHIA, tune DWPYTHIA, tune S0PYTHIA, tune P0SHERPA, with MPIPYTHIA, no MPISHERPA, no MPITotal uncertainty < 90 GeVγT50 < p > 30 GeVjet1Tp < 30 GeVjet2T15 < p > 15 GeVjet3TpS (rad)Δ0 0.5 1 1.5 2 2.5 3Data / Theory0.40.60.811.21.4Data / Theory 0 0.5 1 1.5 2 2.5 3φΔ/d2jγσ) d2jγσ(1/-210-110110               -1 = 1.0 fb intDØ, LDataPYTHIA, tune APYTHIA, tune DWPYTHIA, tune S0PYTHIA, tune P0SHERPA, with MPIPYTHIA, no MPISHERPA, no MPITotal uncertainty < 90 GeVγT50 < p > 30 GeVjet1Tp < 20 GeVjet2T15 < p (rad)φΔ0 0.5 1 1.5 2 2.5 3Data / Theory0.40.60.811.21.4Data / TheoryFig. 2. – On the left: normalized differential cross section in γ+3 jet events, (1/σγ3j)dσγ3j/dΔS,in data compared to MC models, and the ratio of data over theory, only for models includingMPI, in the range 15 < P jet2T < 30GeV. On the right: normalized differential cross section inγ + 2 jet events, (1/σγ2j)dσγ2j/dΔS, in data compared to MC models, and the ratio of dataover theory, only for models including MPI, in the range 15 < P jet2T < 20GeV.PT3 > 40GeV/c. For |y| < 2.4 additional measurements are made for PT3 > 70GeVand PT3 > 100GeV. Figure 3 shows results for the differential three jet cross section inM3j , for different rapidity ranges and for different PT criteria. The data are comparedto theoretical models of NLO pQCD and non-perturbative corrections. The renormal-ization and factorization scales are set to the average PT of the three leading PT jets:μR = μF = μ0 = (PT1+PT2+PT3)/3. Figure 4 shows the ratio between data and theoryFig. 3. – D0 measurement of the three-jet cross section as a function of the three-jet invariantmass in different rapidity regions (left) and for different PT3 requirements (right).144 S. MOED SHERFig. 4. – Ratios between data and theory for the D0 three-jet cross section measurement. Theratios are comupted for different PDFs and are shown as a function of the three-jet invariantmass in different rapidity regions and for different PT3 requirements.for different PFDs. The data are reasonably well described by the next-to-leading ordercalculation done with NLOJET++ and the MSTW2008NLO PDFs.4. – W + jets productionThe measurements of inclusive W (→ eν) + n jets cross sections (n = 1, 2, 3, 4), pre-sented as total inclusive cross sections and differentially in the n-th jet transverse mo-mentum was done by the D0 Collaboration [5]. The measurements are made using datacorresponding to an integrated luminosity of 4.2 fb−1. The selection for W +n jet eventsinclude the following criteria: presence of a central electron with PT > 15Gev, missingtransverse energy > 20GeV, transverse mass of the W boson candidate > 40GeV/c, andthe jet transverse momentum > 20GeV. The spatial distance between the cone and thenearest jet is required to be ΔR > 0.5. Acceptance corrections and background contribu-tions from Z+jets, top pair production, diboson and single top production are estimatedusing different MC events generators [5]. The backgrounds from multijet production aredetermined using aa data driven method. Figure 5 shows these cross section results asa function of PT of the first, second, third and forth jet, and compared to pQCD pre-dictions in NLO (for njet < 3) or LO (for njet = 4). Within their uncertainties, theNLO pQCD predictions agree pretty well with the data, except for the low PT regionfor W + 1 jet and high-PT region for W + 3 jets. The LO predictions for W + 4 jetsagree with the data, but have very large uncertainties from the renormalization scaledependence.5. – Observation of W boson + single-charm productionCalculations of W + heavy quark production are available at leading order (LO) andnext-to-leading order (NLO) QCD [6], with the NLO cross section about 50% larger thanRECENT QCD STUDIES AT THE TEVATRON 145 (GeV)T jet pthn20 30 40 210 210×2 (1/GeV)T/dpσ.dWσ1/-910-810-710-610-510-410-310-210>20 GeVTp>40 GeV, TW|<1.1, meη>15 GeV, | Tep|<3.2jet>20 GeV, |yTjet=0.5, pconeR)+jets+Xν e→, W(-1, 4.2 fb∅DRocket+MCFM Blackhat+SherpaFig. 5. – Measured W + n jet differential cross section as a function of n-th jet PT for jetmultiplicities n = 14, normalized to the inclusive W → e cross section. W + 1 jet inclusivespectra are shown by the top curve, the W + 4 jet inclusive spectra by the bottom curve. Themeasurements are compared to the fixed-order NLO predictions for the jet multiplicities n = 13,and to LO predictions for n = 4.at LO. Overall, the uncertainty on the NLO theoretical expectation for W boson + single-charm quark production at the Tevatron is about 1020%, depending on the charm phasespace, with the largest uncertainties due to the choice of factorization and renormalizationscales and the shape of the s quark PDF.The CDF Collaboration performed the first observation of the pp¯ → Wc productioncross section at the Tevatron collider [7]. The charm quark is identified through thesemileptonic decay of the charm hadron into an electron or muon (soft leptons). The Wcproduction cross section is determined first separately using soft electrons and soft muons,and then the two measurements are combined. The analysis exploits the correlationbetween the charge of the W boson and the charge of the soft lepton from the semileptonicdecay of the charmed hadron. Charge conservation in the process gq → Wc (q = d, s)allows as final states only the pairings W+c¯ and Wc; as a result, the charge of thelepton from the semileptonic decay of the c quark and the charge of the W boson arealways of opposite sign. In practice, this correlation is diluted in the reconstructedevents due to hadronic decays in flight and hadrons misidentified as soft leptons. Thesecontaminations in the signal selection and other background contributions, such as W +jets and Z + jets production, top pair production and single top, as well as dibosonand multijet production, are considered in the analysis. The W is identified throughits leptonic decay. The measured production cross section σWc(PTc > 20GeV/c, |ηc| <1.5) − B(W → lν) = 13.3 + 3.3 pb, in agreement with theoretical expectations, with asignificance for the Wc signal of 6.4σ.146 S. MOED SHERFig. 6. – The angularity distribution for midpoint jets with PT > 400GeV/c. The tt¯ rejectioncuts and requirement for 90GeV < mj1 < 120GeV are applied. The PYTHIA calculation (reddashed line) and the pQCD kinematic endpoints are shown (left); The planar flow distributionsafter applying the top rejection cuts and requiring 130GeV < mj1 < 210GeV. PYTHIA QCD(red dashed line) and tt¯ (blue dotted line) jets are shown (right).6. – Jet substructureThe study of high-transverse-momentum massive jets provides an important test ofpQCD and gives an insight into the parton showering mechanism. In addition, massiveboosted jets compose an important background in searches for various new physics mod-els, the Higgs boson, and highly boosted top quark pair production. Particularly relevantis the case where the decay of a heavy resonance produces high-PT top quarks that decayhadronically. In all these cases, the hadronic decay products can be detected as a singlejet with substructure that differs from pQCD jets once the jet PT is greater than 400–500GeV/c. The CDF Collaboration performed a measurement of substructure of jetswith PT > 400GeV/c by studing distributions of the jet mass and measuring angularity,the variable describing the energy distribution inside the jet, and planar flow, the vari-able differentiating between two-prong and three-prong decays [8]. At small cone sizesand large jet mass, these variables are expected to be quite robust against soft radiationand allow, in principle, a comparison with theoretical predictions in addition to compar-ison with MC results. Jets are reconstructed with the midpoint cone algorithm (coneradii R = 0.4, 0.7, and 1.0) and with the antikt algorithm [9] (with distance parameterR = 0.7). Events are selected in a sample with 6 fb−1 based on the inclusive jet trigger.There is a good agreement between the measurement and the analytic predictions andwith PYTHIA MC predictions. The midpoint and antikt algorithms have very similarjet substructure distributions for high mass jets, see fig. 6. The angularity distributionshown on fig. 6 (left) in addition to reasonable agreement data and PYTHIA MC alsodemonstrates that the high-mass jets coming from light quark and gluon production areconsistent with two-body final states and that further rejection against high mass QCDjets can be obtained by using the planar flow variable, fig. 6 (right).7. – ConclusionsMeasurements from the Tevatron Run II defined a new level of QCD precision mea-surements in hadron-hadron collisions. Several results from the Tevatron were reviewedin this note mostly showing nice agreement with NLO predictions. The QCD programs ofRECENT QCD STUDIES AT THE TEVATRON 147the CDF and D0 Collaborations have been dedicated to testing and constraining pQCDand also measuring cross sections of important background processes. These studies areimportant for many searches at the Large Hadron Collider (LHC), where measurementsof this type are among the first to be made using LHC data [10,11].REFERENCES[1] Acosta D. E. et al. (CDF Collaboration), Phys. Rev. D, 71 (2005) 032001.[2] LeCompte T. and Diehl H. T., Ann. Rev. Nucl. Part. Sci., 50 (2000) 71.[3] Abazov V. M. et al. (D0 Collaboration), Phys. Rev. D, 83 (2011) 052008.[4] Abazov V. M. et al. (D0 Collaboration), arXiv:1104.1986v2 [hep-ex] (2011).[5] Abazov V. M. et al. (D0 Collaboration), Phys. Lett. B, 705 (2011) 200.[6] Keller S., Giele W. T. and Laenen E., Phys. Lett. B, 372 (1996) 141.[7] CDF Collaboration, Public note, http://www-cdf.fnal.gov/physics/new/qcd/QCD.html (2012).[8] Aaltonen T. et al. (CDF Collaboration), arXiv:1106.5952v2 [hep-ex] (2011).[9] Cacciari S. G. P. and Soyez G., JHEP, 04 (2008) 063.[10] CMS Collaboration, CERN-CMS-NOTE-2006, 067 (2007) .[11] Skands P. Z., Contribution to Les Houches Workshop on Physics at TeV CollidersFERMILAB-CONF-07-706-T (2007).

Recent QCD studies at the Tevatron

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Recent QCD studies at the Tevatron

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