aa r X i v : . [ h e p - e x ] A ug W / Z + jet production at the Tevatron Lars Sonnenschein a on behalf of the DØ and CDF collaborations a RWTH Aachen UniversityIII. Phys. Inst. A52056 Aachen, Germany.
Abstract
Vector boson plus jet production is interesting for Higgs search, beyond the Standard Model physics and providesstandard candles for calibration. This is complementary to inclusive jet production measurements which provideprecision tests of perturbative QCD. A multitude of W / Z plus heavy and light flavour jet measurements in p ¯ p collisionsat a centre of mass energy of √ s = .
96 TeV is discussed. Next-to-Leading order perturbative QCD predictions andvarious models are compared to the measurements.
1. Introduction
The discussed measurements are accomplished by themulti-purpose collider experiments DØ and CDF withtheir broad particle identification capabilities throughcentral tracking, fine granulated calorimeters and muonspectrometers. The detectors are located at the Tevatronaccelerator at Fermilab, where proton anti-proton colli-sions take place at a centre of mass energy of 1 .
96 TeV.Vector boson plus jet production at the Tevatron is com-plementary to the kinematic regimes of the HERA ac-celerator and fixed target experiments. It provides han-dles to Parton Distribution Functions (PDF), initial andfinal state gluon radiation and the transverse momen-tum ( p T ) spectra of the jets and the vector bosons. Themeasurements provide standard candles for calibrationand tuning of Monte-Carlo (MC) event generators. Theunderstanding of these processes is important for Stan-dard Model (SM) as well as Beyond the SM (BSM) phe-nomenology. The Tevatron dataset is now large enoughto confront predictions and it has a unique kinematicoverlap with the LHC and the expected SM Higgs massrange.The data of the measurements are fully corrected forinstrumental e ff ects. Therefore they can be directly usedfor testing and improving existing MC event genera-tors and any future calculation and model. Next-to-Leading Order (NLO) and Leading Order (LO) per-turbative QCD (pQCD) predictions from MCFM [1]are compared to data taking non-perturbative e ff ectsof hadronisation and underlying event from simulation into account in the prediction, i.e. the comparison takesplace at the hadronic final state or synonymous at theparticle level. The relative uncertainties of the mea-surements are dominated by the Jet Energy Scale (JES)uncertainty. Iterative seed-based infrared safe midpointcone jet algorithms are used by the DØ [2] and CDF [3]experiments in Run II.In the following sections 2-6 the Tevatron vector bo-son plus light flavour jet measurements are presented,followed by the vector boson plus heavy flavour jet mea-surements in sections 7-11.
2. DØ inclusive Z /γ ∗ ( → ee ) + jet cross section The Z + jet production cross section is measured [4]di ff erentially in inclusive p T bins of leading, second andthird leading jet, making use of an integrated luminosityof 1 . − . Electron / positron candidates above a trans-verse momentum of p T >
25 GeV are selected in anabsolute pseudorapidity range of | η e | < . , . < | η e | < . Z boson candidates in a mass window of65 < M ee <
115 GeV. Jets with a cone radius of R = . p jet T >
20 GeV are selected in a rapidity range of | y jet | < .
5. The cross section is normalised to inclusive Z + jet production which cancels uncertainties on lu-minosity and most of electron trigger and identificationuncertainties. The phase space of the selected events isextrapolated to the full lepton kinematics. While the(N)LO pQCD predictions are in agreement with datathere are large di ff erences between the di ff erent mod-els of PYTHIA [5], HERWIG [6] ( + JIMMY), ALP-
Preprint submitted to Nuc. Phys. (Proc. Suppl.) November 5, 2018
EN [7] + PYTHIA and SHERPA [8]. The experimen-tal errors are small and dominated by statistics, allowingfor future improvements.
3. CDF inclusive Z /γ ∗ ( → ee ) + jet cross section The Z + jet production cross section is measured [9]di ff erentially in inclusive transverse momentum bins ofthe leading and second leading jet, making use of an in-tegrated luminosity of 1 . − . Electron / positron can-didates above a transverse energy of E eT >
25 GeV areselected in an absolute pseudorapidity range of | η e | < . , . < | η e | < . Z boson candidates in amass window of 66 < M ee <
116 GeV. Jets with a coneradius of R = . p jet T >
30 GeV are selected in arapidity range of | y jet | < .
1. There is good agreementbetween data and NLO pQCD prediction.
4. DØ inclusive Z /γ ∗ ( → µµ ) + jet cross section Di ff erential angular distributions of the Z + jet produc-tion cross section is measured [10] in inclusive bins oftransverse Z boson momentum making use of an inte-grated luminosity of 1 . − . Oppositely charged muoncandidates above a threshold of p T >
15 GeV are se-lected in an absolute rapidity range of | y µ | < . Z boson candidates in a mass window of 65 < M µµ <
115 GeV. Jets with a cone radius of R = . p jet T >
20 GeV are selected in a rapidity rangeof | y jet | < .
8. The di ff erential cross section in two in-clusive bins of Z boson transverse momentum ( p ZT >
25 GeV and p ZT >
45 GeV) is measured as a function ofthe angular variables rapidity sum, rapidity di ff erenceand the azimuthal angle di ff erence between the leadingjet and the Z boson. ALPGEN [7] and SHERPA [8]include up to three partons in the matrix element cal-culations. The binning is chosen such, that the detectorresolution causes little migrations between bins. Thereis less agreement between data and predictions in thelower p ZT >
25 bin. This holds for the non-pQCD aswell as for the pQCD predictions. Among the non-pQCD predictions SHERPA (1.1.3) provides the bestdescription of the angular distributions, in particular ∆ y ( Z , j ), in the p ZT >
45 GeV bin. In the p ZT >
25 GeVbin the measured cross section is σ ( Z + jet) /σ ( Z ) = (cid:2) ± ± (cid:3) · − compared to the pQCDNLO prediction of [40 ± ± · − andthe pQCD LO prediction of [40 ± ± · − .
5. CDF Z ( → ee , µµ ) + p T balance CDF measured the Z boson + p T bal-ance [11], making use of an integrated luminosity of4 . − and sets precision limits on the measurementsof Standard Model (SM) jet and vector boson ob-servables, relevant for the discovery potential of newphysics. Oppositely charged lepton candidates ( ℓ = e , µ ) above a threshold of p µ T , E eT >
18 GeV are se-lected to form Z boson candidates in a mass window of80 < M µµ <
100 GeV. A leading jet with a p jet T > . < | η detjet | < . ff erent cone algorithmradii R = . , . , .
0. The azimuthal angle between the Z boson and the jet has to satisfy ∆ φ > . Z boson + jet produc-tion are obtained from PYTHIA [5] and ALPGEN [7].The CDF JES is calibrated via tuning of the calorimeterresponse to single particles. Therefore the Z boson plusjet p T balance provides an independent test of the CDFJES. While the measured track in jet distributions agree (jet1-jet2) [deg] fD D a t a / P r e d i c t i on s (Z)>25 GeV/c, jet cone = 0.4 T Z+jet, P
CDF Run II Preliminary
Figure 1: Leading jet plus Z boson p T balance data over simula-tion (PYTHIA) ratio as a function of the azimuthal angle di ff erencebetween the leading and the second leading jet. Data has more sub-leading jets close in angle to the leading jet. with the quark and gluon jet fractions of PYTHIA [5],a higher rate of sub-leading jets collinear to the leadingjet is observed in data (see Fig. 1). This does set lim-itations on the precision of the JES determined at theATLAS and CMS experiments by means of the jet plus Z boson p T balance of the order of 3%. Only large an-gle final state radiation observed in form of sub-leadingjets turns out to be able to explain the discrepancy.2 . CDF inclusive W ( → e ν ) + n = The W + n jet inclusive production cross section ( n = −
4) is measured [12] di ff erentially in inclusive trans-verse momentum bins of the n th leading jet, makinguse of an integrated luminosity of 320 pb − . Elec-tron / positron candidates above a transverse energy of E eT >
20 GeV are selected in an absolute pseudorapid-ity range of | η e | < .
1. A missing transverse energy of E / T >
30 GeV and a transverse mass of m WT >
20 GeV isrequired to select W boson candidates. Jets with a coneradius of R = . p jet T >
20 GeV are selected in apseudorapidity range of | η jet | < .
0. The measurementbenefits of a production cross section which is about tentimes higher than the one for Z + jets production. Atthe same time the multi-jet and top quark productionbackground needs to be controlled. There is good agree-ment between data and the NLO pQCD prediction. Atlow transverse jet momentum the MC event generatorsALPGEN [7] plus PYTHIA [5] (with MLM matchingof the matrix element to the parton shower) and MAD-GRAPH [13] plus HERWIG [6] (with CKKW match-ing) need a better modelling of the underlying event.
7. DØ inclusive σ ( Z + b ) /σ ( Z + j ) ratio ( Z → ee , µµ ) The inclusive Z + b jet production cross section is mea-sured [14] as the ratio over the inclusive Z + jet pro-duction cross section, making use of an integrated lu-minosity of 4 . − . Z boson decays into a pair ofcharge conjugated electrons or muons are considered.Muon candidates with p µ T >
10 GeV in the pseudora-pidity range of | η det | < . / positron can-didates with p eT >
15 GeV in the pseudorapidity rangeof | η det | < . R = . p jet T >
20 GeV in a pseudorapidity range of | η det | < . b flavour jets are separated from c and light flavourjets by means of a neural network jet tagging algorithmbased on the longer mean lifetime of heavy flavourhadrons with respect to light ones. The flavour frac-tions are determined by a fit of lifetime variable tem-plates to the data. The templates are obtained fromALPGEN [7] plus PYTHIA [5] while the cross sec-tions are taken from NLO pQCD calculations. The mea-sured total cross section ratio is σ ( Z + b ) /σ ( Z + j ) = . ± . ± . . ± .
8. CDF inclusive σ ( Z + b ) /σ ( Z ) ratio ( Z → ee , µµ ) The inclusive Z + b jet production cross section is mea-sured [15] as the ratio over the inclusive Z productioncross section, making use of an integrated luminosity of2 . − . Z boson decays into a pair of charge conju-gated electrons or muons are considered. The cross sec-tion is measured di ff erentially in bins of jet and heavyflavour jet multiplicity, as functions of leading b jettransverse energy and pseudorapidity and as a func-tion of the Z boson transverse momentum. b jets areidentified by means of a secondary vertex tagging al-gorithm. The leading and second leading leptons ( e , µ )are required to satisfy p µ T , E e T >
18 GeV and p µ T , E e T >
10 GeV. The invariant dilepton mass has to lie in the in-terval 76 < M ℓℓ <
106 GeV. Jets with a cone radius of R = . E jet T >
20 GeV are selected in a pseudora-pidity range of | η jet | < .
5. The measured cross sectionratio σ ( Z + b ) /σ ( Z ) = (cid:2) . ± . ± . (cid:3) × − is in agreement with NLO pQCD predictions. Bothdata and theory have large uncertainties. While data un-certainties are statistics dominated the large uncertaintyof the theory prediction arises from the missing NLOpQCD prediction for Z + b ¯ b production which in turncauses a large scale dependence.
9. DØ inclusive σ ( W + c ) /σ ( W + j ) ratio ( W → ℓν ) The inclusive W + c jet production cross section is mea-sured [16] as the ratio over the inclusive W + jet pro-duction cross section, making use of an integrated lumi-nosity of 1 . − . The leptonic W boson decay witha muon / electron in the final state is considered. Thecross section is measured di ff erentially in bins of jet p T .Lepton candidates with p ℓ T >
20 GeV and events with amissing transverse energy of E / T >
20 GeV are selected.Jets with a cone radius of R = . p jet T >
20 GeV areselected in a pseudorapidity range of | η jet | < . W bo-son + c quark production is sensitive to the s quark PDFcontent up to scales of Q = GeV . The charge signof the lepton from the W boson decay is opposite (OS)to the one of the c quark. This information is exploitedin tagging an oppositely charged muon in the jet fromthe c quark fragmentation. The same sign (SS) sub-tracted background is small ( ∼ ffi ciencies. Itamounts to σ ( p ¯ p → W + c − jet) /σ ( p ¯ p → W + jets) = . ± . + . − . (syst.) and is within the largeerrors in agreement with the prediction of 0 . ± .
0. CDF semi-incl. W + c jet cross section ( W → ℓν ) The W + c jet exclusive production cross section is mea-sured [17] for selected events with one or two jets, mak-ing use of an integrated luminosity of 1 . − . Lep-ton candidates with p ℓ T >
20 GeV in the pseudorapid-ity range of | η ℓ | < . E / T >
25 GeV are selected. Jets witha cone radius of R = . p jet T >
20 GeV are se-lected in a pseudorapidity range of | η jet | < .
5. Charmflavour jets are tagged by means of a soft muon in thejet. The OS-SS subtracted data distributions are in goodagreement with the prediction of ALPGEN [7] withPYTHIA [5]. The total measured cross section amountsto σ ( W ( → ℓν ) + c ) = . ± . + . − . (syst.) ± . σ ( W ( → ℓν ) + c ) = . + . − . pb for p c -jet T >
20 GeVand | η c -jet | < .
11. CDF semi-incl. W + b jet cross section ( W → ℓν ) The W + b jet exclusive production cross section is mea-sured [18] for selected events with one or two jets, mak-ing use of an integrated luminosity of 1 . − . Theleptonic W boson decay with a muon / electron in the fi-nal state is considered. Lepton candidates with p ℓ T >
20 GeV and | η ℓ | < . E / T >
25 GeV are selected. Jets witha cone radius of R = . p jet T >
20 GeV are se-lected in a pseudorapidity range of | η jet | < .
0. Bottomflavour jets are tagged by means of a secondary ver-tex tagging algorithm. A maximum likelihood fit to thevertex mass distribution of tagged jets is applied to ex-tract the flavour fractions of the selected data sample.The flavour templates are obtained from ALPGEN [7]with PYTHIA [5] and MADEVENT [19] for single topquark production. The measured total cross section is σ ( W ( → ℓν ) + b ) = . ± . ± . σ ( W ( → ℓν ) + b ) = . ± .
14 pb and the LO prediction of σ ( W ( → ℓν ) + b ) = .
78 pb from ALPGEN. The measuredcross section exceeds the NLO prediction by about three σ standard deviation.
12. Conclusions
Many measurements of vector boson plus light andheavy flavour jet production have been presented. Per-turbative QCD predictions by means of MCFM [1] arein good agreement with data in all inclusive vector bo-son plus jet production measurements. The predictions of ALPGEN and MCFM are about three σ below theexclusive W boson plus b jet cross section measurementof CDF, where a reliable secondary vertex tagger hasbeen used. The jet over Z boson p T balance measure-ment of CDF shows up limitations for the Jet EnergyScale precision at LHC experiments of the order of 3%.The p T imbalance can be explained by large angle fi-nal state radiation in form of collinear sub-leading jets.There is no perfect Monte-Carlo event generator. Thisholds for PYTHIA and HERWIG + JIMMY as well asfor SHERPA and ALPGEN which are superior to theformer parton shower Monte-Carlo event generators. Ingeneral the data are corrected for detector e ff ects, so thatthey can be compared to predictions at the hadronic fi-nal state. This means that the data can be re-used for thetuning of Monte-Carlo event generators at any time inthe future. Acknowledgements
Many thanks to the sta ff members at Fermilab, collab-orating institutions and in particular the DØ and CDFcollaborations. References [1] J. Campbell and R. K. Ellis, Phys. Rev. D , 113007 (2002).[2] G. C. Blazey et al. , in Workshop Proceedings: QCD and WeakBoson Physics in Run II , ed. by U. Bauer, R. K. Ellis and D.Zeppenfeld, FERMILAB-PUB-00-297 (2000).[3] A. Abulencia et al. (CDF collaboration), Phys. Rev. D ,071103(R) (2006), A. Bhatti et al. , Nucl. Instrum. Meth. A. , 375 (2006).[4] V. M. Abazov et al. (DØ collaboration), arXiv:0903.1748v2,FERMILAB-PUB-09-066-E, Phys. Lett. B , 45 (2009).[5] T. Sj¨ostrand et al. , JHEP , 026 (2006).[6] G. Corcella et al. , JHEP , 010 (2001).[7] M. L. Mangano et al. , JHEP , 001 (2003).[8] T. Gleisberg et al. , JHEP , 007 (2009).[9] T. Altonen et al. (CDF collaboration), Phys. Rev. Lett. ,102001 (2008).[10] V. M. Abazov et al. (DØ collaboration), arXiv:0907.4286v2,FERMILAB-PUB-09-373-E, Phys. Lett. B , 370 (2010).[11] T. Altonen et al. (CDF collaboration), prel., CDF note 10082,submitted to Nucl. Instrum. Meth. A (2010).[12] T. Altonen et al. (CDF collaboration), Phys. Rev. D ,011108(R) (2008).[13] F. Maltoni and T. Stelzer, J. High Energy Phys. 02 (2003) 027.[14] V. M. Abazov et al. (DØ collaboration), prel., DØ note 6053-CONF (2010).[15] T. Altonen et al. (CDF collaboration), Phys. Rev. D , 052008(2009).[16] V. M. Abazov et al. (DØ collaboration), arXiv:0803.2259v1,FERMILAB-PUB-08-062-E, Phys. Lett. B , 23 (2008).[17] T. Altonen et al. (CDF collaboration), Phys. Rev. Lett. ,091803 (2008).[18] T. Altonen et al. (CDF collaboration), Phys. Rev. Lett. ,131801 (2010).[19] J. Alwall et al. , Journ. HEP , 028 (2007)., 028 (2007).