Results are presented for the inclusive jet cross section versus jet
transverse energy in proton-antiproton collisions at center of mass energy 1.8
TeV as measured by the CDF and D0 detectors at Fermilab's Tevatron collider.
The data are compared to next-to-leading order QCD predictions using different
input parton distribution functions. The ratio of inclusive jet cross sections
at center of mass energy 0.63 TeV and center of mass energy 1.8 TeV, versus jet
x_T, is also presented and compared to QCD predictions.Comment: Submitted to the proceedings of the XXIX International Symposium on
  Multiparticle Dynamics (ISMD99), Providence, RI. 12 pages including 12
  figure

Seidel, Sally

English

arXiv

Results are presented for the inclusive jet cross section versus jet E{sub T} in p-{bar p} collisions at {radical}s = 1.8 TeV as measured by the CDF and D0 detectors at Fermilab's Tevatron collider. The data are compared to next-to-leading-order QCD predictions using different input parton distribution functions. The ratio of inclusive jet cross sections at {radical}s = 0.63 TeV and {radical}s = 1.8 TeV, versus jet {chi}{sub T}, is also presented and compared to QCD predictions

Seidel, S.

UNT Digital Library

F Fermi National Accelerator LaboratoryFERMILAB-Conf-99/333-ECDF and D0Inclusive Jets at the TevatronS. SeidelFor the CDF and D0 CollaborationsThe University of New MexicoAlbuquerque, New Mexico 87131Fermi National Accelerator LaboratoryP.O. Box 500, Batavia, Illinois 60510November 1999Presented Paper at the 19th International Symposium on Multiparticle Dynamics (ISMD 99),Providence, Rhode Island, August 9-13, 1999Operated by Universities Research Association Inc. under Contract No. DE-AC02-76CH03000 with the United States Department of EnergyDisclaimerThis report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any oftheir employees, makes any warranty, expressed or implied, or assumes any legal liability orresponsibility for the accuracy, completeness, or usefulness of any information, apparatus,product, or process disclosed, or represents that its use would not infringe privately ownedrights. Reference herein to any specic commercial product, process, or service by tradename, trademark, manufacturer, or otherwise, does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the United States Government or any agencythereof. The views and opinions of authors expressed herein do not necessarily state or reectthose of the United States Government or any agency thereof.DistributionApproved for public release; further dissemination unlimited.Copyright NoticationThis manuscript has been authored by Universities Research Association, Inc. under con-tract No. DE-AC02-76CH03000 with the U.S. Department of Energy. The United StatesGovernment and the publisher, by accepting the article for publication, acknowledges thatthe United States Government retains a nonexclusive, paid-up, irrevocable, worldwide licenseto publish or reproduce the published form of this manuscript, or allow others to do so, forUnited States Government Purposes.1CDF/PUB/JET/PUBLIC/5095INCLUSIVE JETS AT THE TEVATRONaSALLY SEIDELThe New Mexico Center for Particle PhysicsThe University of New MexicoAlbuquerque, NM 87131 USAfor the CDF and D0 CollaborationsResults are presented for the inclusive jet cross section versus jet ET in p  p col-lisions atps = 1:8 TeV as measured by the CDF and D0 detectors at Fermilab'sTevatron collider. The data are compared to next-to-leading-order QCD predic-tions using dierent input parton distribution functions. The ratio of inclusive jetcross sections atps = 0:63 TeV andps = 1:8 TeV, versus jet xT , is also presentedand compared to QCD predictions.1 IntroductionJet distributions at colliders are interesting to study for several reasons, inparticular because they can signal the existence of new phenomena, test QCDpredictions, and validate parton distribution functions. The complementaryTevatron detectors D0 1 and CDF 2 have studied the inclusive jet cross sectionat center-of-mass energies 1800 and 630 GeV.The aspects of the two experiments that are especially important forthe jet analyses are well described elsewhere 3. For the results presentedhere, the radius of the reconstruction cone used 4;5 in both analyses is R p()2 + ()2 = 0:7, where  is track pseudo-rapidity,  is measured fromthe Tevatron plane,  = 2   1,  = 2   1, and the subscripts 1 and 2correspond to the axis of the cone and the particle track, respectively.2 The Inclusive Jet Cross Section Versus ET atps = 1800 GeVFor jet transverse energies achievable at the Tevatron, the inclusive jet crosssection probes distances down to 10 17 cm. For massless jets and 2 accep-tance in , this cross section, Ed3=dp3, can be written as the product:Ed3dp3=12ETd2dET d:aPublished in the Proceedings of the XXIX International Symposium on Multiparticle Dy-namics (ISMD99), Providence, RI, 1999.CDF/PUB/JET/PUBLIC/5095 2The second factor can be written in terms of the natural experimental variables:d2dET d=NETL;where N is the number of jets observed, ET is the transverse energy bin size(5{80 GeV),  is the pseudorapidity bin size (1.2), and L is the luminosity.CDF and D0 begin their analyses with similar data quality requirements.Both dene the z-axis as the direction of the proton beam and place a cut onthe absolute value of the z-coordinate of the primary vertex in the event inorder to maintain the projective geometry of the calorimeter towers. CDF re-quires jzvertexj < 60 cm; D0 requires jzvertexj < 50 cm. To restrict the study toevents whose energy is fully contained in the central barrel calorimeter, CDF(D0) requires that jets have pseudorapidity (detector) relative to the detector-based coordinate system such that 0:1(0:0)  jdetectorj  0:7(0:5). To rejectbackground due to accelerator loss, CDF further requires explicitly that thetotal energy in the event be less than 1800 GeV. Both experiments place cutson the missing transverse energy (6 ET ) in the event in order to reject cosmicrays and mis-vertexed events. CDF requires that 6 ET =pPallET < 6, whileD0 requires that 6 ET < 30 GeV or 0:3Eleading jetT , whichever is larger. Bothexperiments also place cuts on the ratio of energies detected by the electro-magnetic and hadronic calorimeters and on jet shapes, in order to suppressbackground from noise.The two experiments next correct for pre-scaling of triggers, detection e-ciencies (these are typically in the range 94{100%), and \smearing,"6;7 the lastof which concerns the combined eect upon the data of energy mismeasurementand detector resolution. No correction is made for jet energy deposited outsidethe cone by the fragmentation process, as this is included in the next-to-leadingorder (NLO) calculation to which the data are ultimately compared.Figure 1 shows the CDF measurement 8 of the inclusive jet cross sectionfor collisions atps = 1:8 TeV. This gure includes data measured in Runs 1aand 1b. The data are compared to the prediction by the NLO calculation byEllis, Kunszt, and Soper (EKS) 9, in which the CTEQ4M 10 parton distribu-tion function (PDF) has been used and the renormalization and fragmentationscales have both been set equal to ET =2.Figure 2 shows the quantity (DATA THEORY)=THEORY for the samedata for cases in which the PDF is CTEQ4M, CTEQ4HJ 10, and MRST 11.Application to this analysis of the CTEQ4A and MRST PDF families has alsobeen examined.The eects on the cross section of a 1 change in each of the CDF system-atic uncertainties are shown in Figure 3. These uncertainties, which are fullyCDF/PUB/JET/PUBLIC/5095 3Figure 1: The preliminary measurement by CDF of the inclusive jet cross section forps =1:8 TeV, compared to the NLO EKS prediction with input parton distribution functionCTEQ4M.Figure 2: The percentage dierence between the inclusive jet cross section as measured byCDF atps = 1:8 TeV (\DATA"), and the EKS NLO prediction (\THEORY"), for a varietyof input parton distribution functions.CDF/PUB/JET/PUBLIC/5095 4correlated from bin to bin but are completely uncorrelated with each other,include the calorimeter's response to charged hadrons and showering particles,the stability of the energy scale, the details of the jet fragmentation model usedin the simulation, the energy associated with the underlying event in the re-construction cone, the modelling of the jet energy resolution function requiredfor unsmearing, and the normalization. The excess at high values of ET thatis present in the Run 1b data is consistent with what was previously observedin the Run 1a data. The analysis of the Run 1a excess has been describedpreviously 12. Quantitative comparison of the CDF Run 1b data with theoryis now underway.Systematic uncertainties (CDF Preliminary)-20020 (a) High P T Hadron response-20020 (b) Low P T Hadron response-20020 (c) Energy Scale Stability-20020 (d) Fragmentation-20020 (e) Underlying Event-20020 (f) Electron/Photon Response-20020100 200 300 400(g)Calorimeter ResolutionTransverse Energy (GeV)Percentage change in cross section-20020100 200 300 400(h) NormalizationTransverse Energy (GeV)Figure 3: The percentage change in the Run 1b inclusive jet cross section, as measured byCDF, in response to a 1 standard deviation change in each of the systematic uncertainties.Figure 4 shows the D0 measurement 13 of the inclusive jet cross section.The data are compared with the NLO calculation JETRAD 14 with PDFCTEQ3M 15 and both scales set to one-half the maximum transverse energyassociated with a jet in the event.Figure 5 shows the quantity (DATA THEORY)=THEORY for the samedata for cases in which the PDF is CTEQ3M, CTEQ4M, and MRST.The systematic uncertainties associated with the D0 measurement are dis-played in Figure 6 and concern the calorimeter energy scale, the jet selectionprocedure, the uncertainties on trigger prescale values (denoted as the relativeluminosity), the choice of jet energy resolution function used for unsmearing,and the luminosity. These uncertainties are all fully or partially correlated.CDF/PUB/JET/PUBLIC/5095 5ET (GeV)1/(∆η∆ET)∫∫d2σ/(dE Tdη)dE Tdη  (fb/GeV)DØ Data |ηjet| < 0.5JETRADCTEQ3M, µ = 0.5 ET    max11010 210 310 410 510 610 750 100 150 200 250 300 350 400 450 500Figure 4: The measurement by D0 of the inclusive jet cross section forps = 1:8 TeV, com-pared to the NLO prediction JETRAD with input parton distribution function CTEQ3M.The error bars indicate the statistical error, and the band represents the systematic.|ηjet| < 0.5CTEQ3M(Data-Theory)/TheoryCTEQ4MET (GeV)MRST-0.2500.25-0.2500.25-0.2500.250.550 100 150 200 250 300 350 400 450Figure 5: The percentage dierence between the inclusive jet cross section as measured byD0 atps = 1:8 TeV (\DATA"), and the JETRAD NLO prediction (\THEORY"), for avariety of input parton distribution functions.CDF/PUB/JET/PUBLIC/5095 6ET (GeV)Cross Section Uncertainty (%)Total ErrorEnergy Scale (partially correlated)Overall Luminosity (fully correlated)Relative Luminosity (partially correlated)Resolution (fully correlated)Jet Selection (fully correlated)0510152025303550 100 150 200 250 300 350 400 450Figure 6: Contributions to the D0 inclusive jet cross section uncertainty.The D0 Collaboration has conducted a comparison between the D0 dataand theory. They dene 2  Pi;j(Di   Ti)(C 1)ij(Dj   Tj); where i is binnumber, D is the number of jets observed in the data, T is the number of jetspredicted by the theory, and C is a covariance matrix which was constructedby analyzing the correlation of uncertainties between each pair of ET values.(Bin-to-bin correlations for representativeET bins are about 40% and positive.)There are 24 degrees of freedom (dof). Comparison of the data to the JETRADcalculation for 5 PDF's yields 2=dof values that correspond to probabilitiesof agreement in the range 47{90% for jj  0:5, and 24{72% for 0:1  jj 0:7. Comparison of the D0 data to the EKS calculation using CTEQ3M,Rsep = 1:3R, and scales  = cEmaxT or cEjetT ; for c = 0:25, 0.5, and 1.0, yieldprobabilities greater than or equal to 57% for all cases.There is excellent agreement between the nominal CDF and D0 cross sec-tion values for ET  350 GeV. To quantify the level of agreement over thefull ET range, D0 carried out a 2 comparison between the D0 data and thenominal curve describing the central values of the CDF Run 1b data. The re-sult was a 2=dof = 41:5=24. As this comparison involved the nominal valuesof the CDF data, uncertainties on the CDF central values were not included.To approximate a comparison of the two data sets that includes informationabout the uncertainties on both, one can nd the value of the CDF curve ateach of the D0 ET points, multiply the D0 statistical errors byp2, and removethe 2.7% relative normalization dierence, between the two experiments, as itsCDF/PUB/JET/PUBLIC/5095 7origin is understood; this yields a 2 of 35.1. One can then add systematicerror information by expanding the covariance matrix to include both D0 andCDF uncertainties|this yields a 2 of 13.1, corresponding to a probability ofagreement of 96%.3 The Inclusive Jet Cross Section Versus ET atps = 630 GeVOne can multiply both sides of the inclusive jet cross section formula by E4Tto obtain the dimensionless cross section, d, which is dened asd  E4T (Ed3dp3):One can also dene the scaled transverse energy of a jet, xT  2ET =ps:While the Naive Parton Model predicts that d is independent ofps whenplotted versus xT (the hypothesis of scaling), QCD predicts scaling violationdue to the energy scale dependence of the probability for gluon radiation froma primary parton in the collision. A comparison of d measured at two dierentcenter-of-mass energies by the same experiment suppresses many theoreticaland experimental uncertainties.CDF and D0 collected 576 nb 1 and 537 nb 1 of data, respectively, atps = 630 GeV. (Results from a data set of 8.6 nb 1 collected atps = 546GeV were published 7 by CDF previously.) The data taken atps = 630and 1800 GeV were analyzed by the same method, the only dierence in theanalyses being the treatment of the correction for the energy of the underlyingevent, as this correction is known to increase withps.Figure 7 shows the results of the studies 16;17 with both sets of data nor-malized to theoretical calculations; in the case of D0, JETRAD is used, whilein the case of CDF, EKS. Both calculations take the PDF MRSA0 18.The CDF systematic errors are shown separately in Figure 8. The CDFand D0 measurements agree with each other above about 80 GeV. While nalconclusions must await further studies of the systematic errors, preliminaryresults indicate that the data may diverge in the lowest few ET bins. Whilethe measurements are consistent with each other above 80 GeV, the theoreticalcalculation is somewhat higher for ET < 80 GeV. Additional studies are neededfor energy scale determination at low ET before denitive conclusions can bedrawn.4 The Ratio of the Dimensionless Cross Sections Versus xTFigure 9 shows the ratio of dimensionless cross sections versus jet xT as mea-sured 17 by D0, compared to the JETRAD prediction for 7 combinations ofCDF/PUB/JET/PUBLIC/5095 8CDFD∅  and        systematic uncertainty-0.4-0.200.20.40.60.8120 40 60 80 100 120 140Fractional Deviationµ = Et/2Figure 7: Preliminary D0 and CDF cross sections measured atps = 630 GeV and comparedto NLO QCD predictions. The shaded region indicates the D0 systematic errors.Figure 8: The percentage change in the inclusive jet cross section, as measured by CDF atps = 630 GeV, in response to a 1 standard deviation change in each of the systematicuncertainties.CDF/PUB/JET/PUBLIC/5095 9PDF and scale. In each case the same value is used for the renormalizationand the factorization scale at both values ofps. In all of these cases, the prob-ability that the data and the theory are consistent lies in the range 0.01{7.2%.Figure 9: The preliminary measurement by D0 of the ratio of dimensionless cross sectionstaken atps = 630 and 1800 GeV, compared to the NLO JETRAD prediction, for variouscombinations of parton distribution functions and scales.Figure 10 shows the fractional error on the ratio per bin in jet xT and thebin-to-bin correlation of those errors.D0 has also considered the case in which the scales areps-dependent.They nd, for example, that the combined choice of  = 2ET atps = 630GeV and  = ET =2 atps = 1800 GeV produces a prediction that has 95%probability of consistency with the data. D0 interprets this possible preferenceof the data for two dierent scales as an indicator that the next-to-next-to-leading-order terms in the matrix element for this process, when calculated,may not be negligible.Figure 11 shows the CDF measurement 16 of the ratio of dimensionlesscross sections versus jet xT . Both the 630 GeV and the 546 GeV data arepresented and are consistent. The measurements are compared to the EKSprediction for four choices of PDF and scale. In all four cases the same scaleis used at both values ofps. The systematic errors on the CDF measurementare shown in Figure 12.The ratio measurements by CDF and D0 are consistent for values of jetxT greater than 0.1. The discrepancy between the two data sets below thatpoint may be traced to the measurement of d atps = 630 GeV and was alsoapparent in theps = 546 GeV data. There is, in addition, a slight overallCDF/PUB/JET/PUBLIC/5095 1000.050.10.150.20.05 0.1 0.15 0.2 0.25 0.3Other SystematicsTotal Energy Scale UncertaintyResolution UncertaintyTotal Systematic Uncertainty bandJet xTFractional ErrorBin Number Bin NumberCorrelation0 5 10 15 2001020-0.200.20.40.60.81Figure 10: Top: the fractional error per xT bin on the D0 measurement of the inclusive jetcross section atps = 630 GeV; bottom: the bin-to-bin correlation on the errors shown inthe upper plot.Figure 11: The preliminary measurement by CDF of the ratio of dimensionless cross sectionstaken atps = 630 and 1800 GeV, compared to the EKS NLO prediction, for variouscombinations of parton distribution functions and scales.CDF/PUB/JET/PUBLIC/5095 11Figure 12: The percentage change in the ratio of dimensionless cross sections, as measured byCDF, in response to a 1 standard deviation change in each of the systematic uncertainties.normalization dierence of about 20% between the theoretical predictions andthe measurements.AcknowledgementsThe author wishes to thank members of the CDF and D0 Collaborations,particularly Brenna Flaugher, Gerald Blazey, John Krane, Alexander Akopian,Robert Hirosky, Joey Huston, Andrew Brandt, Anwar Bhatti, and Greg Snow,for their advice on the presentation of these results.References1. S. Abachi et al., Nucl. Instr. and Meth. A 338, 185 (1994).2. F. Abe et al., Nucl. Instr. and Meth. A 271, 387 (1988) and referencestherein; F. Abe et al., Phys. Rev. D 50, 2966 (1994); C. Haber et al.,Nucl. Instr. and Meth. A 289, 388 (1990).3. G. C. Blazey and B. L. Flaugher, FERMILAB-PUB-99-038-E (1997).4. B. Abbott et al., FERMILAB-PUB-97-242-E (1997).5. F. Abe et al., Phys. Rev. D 45, 1448 (1992).6. M. Bhattacharjee, Ph. D. thesis, University of Delhi, 1996, unpublished.CDF/PUB/JET/PUBLIC/5095 127. F. Abe et al., Phys. Rev. Lett. 70, 1376 (1993).8. R. Hirosky and F. Bedeschi, Proc. Hadron Collider Physics WorkshopXIII, Bombay, 1999.9. S. D. Ellis, Z. Kunszt, and D. E. Soper, Phys. Rev. Lett. 64, 2121 (1990).10. H. L. Lai, et al., Phys. Rev. D 55, 1280 (1997).11. A. D. Martin, et al., Eur. Phys. J. C 4, 463 (1998).12. F. Abe et al., Phys. Rev. Lett. 77, 438 (1996).13. B. Abbott et al., Phys. Rev. Lett. 82, 2451 (1999).14. W. T. Giele, E. W. N. Glover, and D. A. Kosower, Phys. Rev. Lett. 73,2019 (1994).15. H. L. Lai et al., Phys. Rev. D 51, 4763 (1995).16. J. Huston, Proc. 29th Int. Conf. on High Energy Physics, Vancouver,1998.17. G. Blazey, Proc. 29th Int. Conf. on High Energy Physics, Vancouver,1998.18. A. D. Martin, R. G. Roberts, and W. J. Stirling, Phys. Lett. B 354, 154(1995).

Inclusive Jets at the Tevatron

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