CDF note 874 Measurement of the Inclusive Jet Cross Section Using the Midpoint Algorithm in Run II at CDF he CDF Collaboration URL http://www-cdf.fnal.gov (Dated: July 5, 006) We present a preliminary measurement ofthe inclusive jet cross section using the Midpoint jet clustering algorithm in five different rapidity regions up to jy j = :. his is the first analysis which measures the inclusive jet cross section using the Midpoint algorithm in the forward region. he results are based on over fb ofcdf Run II data. hey are consistent with NLO pqcd predictions from EKS with CEQ6. parton density functions. Preliminary Results for Summer 006Conferences
I. INRODUCION he measurement of the differential inclusive jet cross section at CDF reaches the highest momentum transfers ever directly studied in collider experiments, and thus it is potentially sensitive to new physics such as quarksubstructure [, ]. Studying the highest energy events at the evatron is equivalent to probing distances of the order of 9 m. his measurement is also a fundamental test of perturbative QCD (pqcd) [, 4]over about eight orders of magnitude in cross section. It spans over 600 GeV/c in jet transverse momentum ( ) and can therefore be used to observe the running of ff s. he inclusive jet measurement can also be used to constrain the (anti)proton PDF which inturn improves the theoretical predictions in all physics channels for experiments at the evatron and future experiments at the LHC. Because the inclusive jet measurement in the forward region probes a kinematic region which is not expected to be sensitive to new physics, it should lead to a powerful constraint on the gluon PDF. his is important because the gluon PDF is very poorly constrained at high x [5] and is the dominant source of theoretical uncertainty in the inclusive jet cross section and many other processes at hadron colliders. In Run I, CDF measured the inclusive jet cross section in the central region of the detector (0: < j j < 0:7) using a cone jet clustering algorithm [6]. A new inclusive jet cross section measurement in the central region (0: < jy j < 0:7) using the Midpoint jet algorithm in Run II has been recently submitted for publication by CDF [7]. hisnoteisan update of the previous analysis with more than twice the integrated luminosity and including the forward rapidity region (jy j < :)[7]. he Midpoint jet finding algorithm is described in detail elsewhere [8, 9]. CDF also recently published an inclusive jet measurement in the central region for jets clustered by thek algorithm []. he rest of this document proceeds as follows. Section II describes the CDF detector components most relevant to this analysis. In section III details of the data sample included in the analysis are discussed. Section IV explains the corrections used to unfold the CDF data to the hadron level so that it may be compared directly with the predictions of pqcd. he Monte Carlo (MC) and CDF detector simulation that are used to derive these corrections are also discussed in this section. Systematic uncertainties on the final cross section measurement are discussed in section V. Finally, in sections VI and VII the results are presented and compared with pqcd predictions. Conclusions are drawn in section VIII. II. HE CDF DEECOR he CDF detector is described in detail in [, ]. Here those components that are crucial to this measurement are briefly discussed. he central detector consists of a silicon vertex detector inside a cylindrical drift chamber. Surrounding the tracking detectors is a superconducting solenoid which provides a.4 magnetic field. Outside the solenoid is the central calorimeter divided into electromagnetic (CEM) and hadronic (CHA) sections. he central calorimeter covers a pseudorapidity range up to.. he CEM is a lead-scintillator calorimeter with a depth of about 8 radiation lengths; the CHA is an iron-scintillator calorimeter with a depth of approximately 4.7 interaction lengths. he energy resolution of the CEM for electrons is ff(e )=E = :5 %= p E (GeV) Φ % while the average energy resolution of the CHA for charged pions is ff(e )=E = 50 %= p E (GeV) Φ %. he forward region, : < j j < :6, is covered by the Plug Calorimeters" consisting of lead-scintillator for the electromagnetic section (PEM) and iron-scintillator for the hadronic section (PHA). he energy resolution of the PEM for electrons is ff(e )=E =6%= p E (GeV)Φ % while the average energy resolution of the PHA for charged pions is ff(e )=E = 80 %= p E (GeV) Φ 5%. he region between the central and forward calorimeters, 0:7 < j j < :, is covered by an iron-scintillator hadron calorimeter (WHA). he WHA has a depth of approximately 4.5 interaction lengths, and a resolution for charged pions of ff(e )=E =75%= p E (GeV) Φ %. III. DAA SAMPLE & EVEN SELECION his analysis includes data taken from February 00 until November 005 and corresponds to an integrated luminosity of.04 fb. he jet data used in this analysis were collected using four paths in the CDF three-level trigger system []. he flow of the four jet trigger paths used in this analysis is shown in figure. he Level trigger requires a calorimeter trigger tower to have eithere > 5GeVorE > GeV. At Level, the calorimeter towers are clustered using a nearest neighbor algorithm. Four trigger paths with cluster E > 5, 40, 60, and 90 GeV are used. Events in these paths are required to pass jet E > 0, 50, 70, and 0 GeV thresholds at Level, where the clustering is performed using a cone algorithm with a cone radius R cone =0:7.
Raw Event Data L S5 (0,50) S L CL5 (, 5) CL40 (,5) CL60 (8) CL90 L J0 J50 J70 J50 Data set: Jet 0 Jet 50 Jet 70 Jet 0 FIG. : rigger flow diagram for the four jet triggers. Prescales are given in parentheses. Ifmultiple prescales are shown then the prescale for that trigger was changed during the data taking period. Cosmic ray and other backgrounds are removed by applying a missing E significance [8] cut. his cut varies according to the jet sample and it is 4, 5, 5, and 6 GeV = for jet0, 50, 70, and 0 triggers respectively. In order to ensure that particles from the pμp interactions are well measured by the CDF detector, primary vertices are required to have jzj < 60 cm. he jet0, 50 and 70 triggers are prescaled to avoid saturating the bandwidth of the trigger and data acquisition system. he jet70 trigger is prescaled by a constant factor of 8 for all data used in this analysis. he prescale for the jet0 and 50 triggers have changed during the data taking period considered. he effective prescales of the jet0 and 50 triggers for all the data were found to be 776:8 and:6, respectively, by luminosity-weighting the inverse of prescale factors, i.e. =P effective ==L total Pi (L i=p i ) where P effective is the effective prescale, L total is the total integrated luminosity, andl i is the integrated luminosity of a period when a prescale factor P i is used. As a cross-checkof the jet0 and jet50 effective prescales, the cross section ratios (before prescale correction) of jet70 to jet0 triggers and of jet70 to jet50 triggers in the jet region where jet70 is efficient were studied, and results were found to be consistent to better than %. he jet yield distributions as function of in the central region (0: < jy j < 0:7) before and after correcting for trigger prescales are shown in figure. he inclusive differential jet cross section is defined as: d ff d dy = Y R Ldt N jet =ffl ; () where N jet is the number of jets in the range, ffl is the trigger and vertex cut efficiency, R Ldt is the effective integrated luminosity which is corrected for trigger prescales, and Y is the rapidity interval. A trigger efficiency greater than 99:5 % is required to include the jets collected by a given jet trigger. Figure shows the raw inclusive differential jet cross section for the five rapidity regions: jy j < 0:, 0: < jy j < 0:7, 0:7 < jy j < :, : < jy j < :6, and :6 < jy j < :. IV. CORRECIONS he jet energy measured by the calorimeters must be corrected for detector effects, such as calorimeter non-linearity and energy smearing, before comparing experimental measurements with theoretical predictions. Figure 4 describes the jet correction scheme used to obtain results corrected to the hadron or parton level [9]. First, an -dependent relative correction is applied to the data and MC (the data and MC corrections are slightly different) in order to equalize the response of the CDF calorimeters to jets in Y. he equalized jet is then corrected for the pileup effect, i.e. the effect of additional pμp interactions in the same bunch crossing. hen, the average (absolute) correction is applied to correct on average for the hadron energy that is not measured by the calorimeter. After that, the hadron
4 Number of Jets 9 8 7 6 5 4 - L=.04 fb 0.< Y <0.7 Midpoint (R =0.7) cone Jet0 (prescale=776.8) Jet50 (prescale=.6) Jet70 (prescale=8) Jet0 (prescale=) 0 0 00 00 400 500 600 700 Uncorrected Number of Jets Prescale 9 8 7 6 5 4 - L=.04 fb Midpoint (R =0.7) cone Jet0 (prescale=776.8) Jet50 (prescale=.6) Jet70 (prescale=8) Jet0 (prescale=) 0.< Y <0.7 0 0 00 00 400 500 600 700 Uncorrected FIG. : Jet yield distributions as a function of in the central region (0: < jy j < 0:7) before (left) and after (right) correcting for trigger prescales. d dydp σ - - - -4 Uncorrected Cross Section (statistical errors only) L=.04 fb - Midpoint (R =0.7) cone Y <0. 0.< Y <0.7 0.7< Y <..< Y <.6.6< Y <. -7-8 0 0 00 00 400 500 600 700 Uncorrected FIG. : Measured raw jet cross section for the five rapidity regions. he raw jet cross section has not been corrected to remove detector effects. and calorimeter level jet distributions are compared in Monte Carlo to derive a bin-by-bin correction in order to remove resolution effects (unfolding). At this point, the data has been corrected to the hadron level. In order to compare directly with pqcd predictions, the effect of the underlying event (UE) and hadronization needs to be removed from the data. After this final correction, data is corrected to the parton level. he Monte Carlo simulation used to derive the corrections, and the details of each correction step are described below.
5 Raw Data Relative Pileup Absolute Bin-by-bin Hadron Level UE/Hadronization Parton Level FIG. 4: Flow diagram for the jet corrections used in the inclusive jet analysis. Correction steps are shown in red, while the hadron level and parton level corrected states are shown in blue. Relative, pileup and average (absolute) corrections are applied directly to the jet before binning. A. Monte Carlo Simulation he parton shower MC programs PYHIA 6. [4] and HERWIG 6.4 [5] along with the CDF detector simulation are used to derive the various corrections which are applied to the data, and to estimate systematic uncertainties. Structure functions for the proton and anti-proton are taken from CEQ5L [6]. he CDF detector simulation is based on GEAN [7] in which a parametrized shower simulation, GFLASH [8], is used to simulate the energy deposited in the calorimeter [9]. he GFLASH parameters are tuned to test-beam data for electrons and high momentum charged pions and to the in-situ collision data for electrons from Z decays and low momentum charged hadrons. However, the CDF simulation does not describe energy deposition in calorimeters perfectly, especially in the regions corresponding to the plug calorimeters and cracks between calorimeter modules. Since the MC simulation is used to derive various jet corrections to be made on data, differences between the real calorimeter response to jets and the calorimeter simulation need to be well understood. Differences in the relative jet energy response and jet energy resolution between the collision data and MC simulation events were investigated using dijet balancing in dijet events [9] and the bisector method [0], respectively. Comparisons of dijet balance between data and MC show that the relative jet energy scale versus is different between data and MC and the difference depends on jet at high rapidity (jy j > :). For example, the jet energy scale in the plug calorimeter region is higher in MC than in data by ο % and the difference increases slightly with jet. his difference is accounted for by the relative corrections which are described in detail in section IV B. he bisector method allows one to compare the energy resolution of the CDF detector and the CDF detector simulation. In the central region (0: < jy j < 0:7) the detector simulation reproduces the detector jet energy resolution well. In the other rapidity regions, small differences were found between data and MC; to account for these differences, modifications to the unfolding factors were derived (< 6%in most bins, and still < % in the most extreme cases). B. Relative Correction he calorimeter response to jets is not flat in. he non-uniformity in arises from cracks between calorimeter modules and also from the different responses of the central and plug calorimeters. he relative correction is introduced to make the jet energy response flat in. he leading two jets in dijet events are expected to be balanced in in absence of QCD radiation. his
balance provides a useful tool to study the jet energy response as a function of and to derive the relative correction. o determine the -dependent relative jet energy correction, we define a jet with 0: < j j < 0:6 (where the CDF calorimeter response to jets is well understood and almost flat in ) as a trigger jet and define the other jet as a probe jet. he balance of these two jets as function of the probe jet provides the relative correction [9]. By making a spline fit to the dijet balance distribution at a given jet,we obtained the -dependent relative corrections. Since the relative jet energy response is different between data and MC, corrections are derived separately for data and MC. As mentioned earlier, the data-mc difference in the relative jet energy scale depends on jet at jy j > :. herefore, another -dependent correction derived for the two corresponding regions is applied to the MC to match the data at any jet. At high, due to lackof statistics in data, there is a large uncertainty inthis -dependent correction. 6 C. Pileup Correction Extra pμp interactions in the same bunch crossing produce some extra energy that contributes to the jet energy. he number of reconstructed primary vertices is a good estimator of the number of interactions in the same bunch crossing. he correction for the additional pμp interactions is derived by measuring in a randomly chosen cone as a function of the number of primary vertices in minimum bias events. he in the randomly chosen cone scales linearly with the number of additional primary vertices in the event. he pileup correction is derived from the slope of this line which estimates the average to be subtracted per additional primary vertex reconstructed in the event. D. Absolute Correction As hadrons pass through the CDF calorimeter, all of their energy is not collected. his effect is mostly due to the non-compensating nature of the calorimeters. he absolute correction corrects the jet for the average energy loss and is derived by comparing hadron level and calorimeter level jets using PYHIA and the CDF detector simulation. Hadron level and calorimeter level jets are matched by their position in the Y ffi space ( R = p Y + ffi» 0:7). he average hadron level jet energy is then studied as a function of the calorimeter jet energy in each rapidity region. his distribution is fit to a fourth order polynomial and the fit is applied as a correction to the of each jet in the data sample. E. Unfolding Correction he next step in correcting the jet distribution to the hadron level is the unfolding correction which removes smearing effects of the calorimeter. he hadron level and calorimeter level (after the absolute correction has been applied) distributions from PYHIA MC are compared on a bin-by-bin basis to derive the correction. After the unfolding correction is applied to the data, the measurement has been corrected to the hadron level. It is now possible to compare the data directly with PYHIA at the hadron level. In all rapidity regions the PYHIA distribution falls off faster than the data at high. his is due to the fact that the PYHIA samples were generated with the CEQ5L PDF which do not include the enhanced high x gluon distribution that was needed to fit Run I inclusive jet data [6, ]. As PYHIA is used to correct the data backto the hadron level, the shapes of the predicted distributions should be the same as that seen in the data in order to avoid introducing any bias. he ratios of data corrected to the hadron level divided by thepyhia predictions are fit to polynomials and used to re-weight the PYHIA distributions to make the shapes agree with the data. he unfolding correction factors obtained from the weighted PYHIA distributions is applied to the data. he change due to the re-weighting of PYHIA is small except for the region 0:7 < jy j < : athigh where the correction is still less than 6 %. F. Hadron to Parton Correction When the absolute and smearing corrections have been applied to the data, it has been corrected to the hadron level. Before it can be directly compared to pqcd theoretical predictions, the effects of the UE and fragmentation must be removed. he hadron to parton level correction is obtained from comparing PYHIA-une A [] MC results at the hadron and the parton level (before fragmentation into hadrons and without multiple parton interactions) to derive abin-by-bin correction. une A has been tuned to fit the underlying event measured at CDF [0]. It is used for all
7 C h p.5.4... 0.9 0.8 0.7 0.6 Midpoint R cone =0.7, f merge =0.75, Y <0. Hadron- to Parton-level Correction Uncertainty 0 0 00 00 400 500 600 700 C h p.5.4... 0.9 0.8 0.7 0.6 Midpoint R cone =0.7, f merge =0.75, 0.< Y <0.7 Hadron- to Parton-level Correction Uncertainty 0 0 00 00 400 500 600 700 C h p.5.4... 0.9 0.8 0.7 0.6 Midpoint R cone =0.7, f merge =0.75, 0.7< Y <. Hadron- to Parton-level Correction Uncertainty 0 0 00 00 400 500 600 700 C h p.5.4... 0.9 0.8 0.7 0.6 Midpoint R cone =0.7, f merge =0.75,.< Y <.6 Hadron- to Parton-level Correction Uncertainty 0 0 00 00 400 500 C h p.5.4... 0.9 0.8 0.7 0.6 Midpoint R cone =0.7, f merge =0.75,.6< Y <. Hadron- to Parton-level Correction Uncertainty 0 0 00 00 400 500 FIG. 5: Hadron to parton level correction applied for each rapidity region. he difference between HERWIG and PYHIA predictions for this correction is conservatively taken as the systematic uncertainty (shaded bands). PYHIA calculations mentioned in this text, but is especially important for the UE correction []. he hadron to parton level correction derived from PYHIA is shown in figure 5. V. SYSEMAIC UNCERAINIES he main sources for systematic uncertainty in the analysis are summarized below: ffl Jet energy scale: he systematic uncertainty due to the jet energy scale is dominant inmost regions. he uncertainty in the jet energy scale is dominated by the uncertainty in the calorimeter simulation tuning in the central region 0: < j j < 0:6 based on the response to individual particles. his uncertainty is less than % of the jet energy and is expressed in a functional form [9]. he corrected jet in the PYHIA MC with detector simulation was varied according to this parametrization and the result was compared with the central value. he systematic uncertainty onthecross section measurement varies from % at low up to 60 % at high in some rapidity regions. here is also an important uncertainty on the jet energy scale due to the correction to the MC based on the dijet balance in the higher rapidity regions (jy j > :) at high. his uncertainty arises from the lackof statistics and is approximately 40 % in the highest bins. ffl Unfolding: he difference between PYHIA and HERWIG is used as the systematic uncertainty on the unfolding correction as they have different fragmentation models. he systematic uncertainty on the measured cross section is taken from the ratio of the unfolding factors obtained from PYHIA and HERWIG. he
difference in the unfolding factors as obtained with weighted and un-weighted PYHIA is also taken as a systematic uncertainty. ffl Jet energy resolution: Due to the sharply falling spectrum of the inclusive jet cross section, any imperfection in the jet energy smearing of the detector simulation will affect the derived unfolding correction. Here the calorimeter level jets in the PYHIA simulation have been smeared by a Gaussian by an extra %. he effect of this extra smearing on the distribution compared with the central measurement is taken as the systematic uncertainty on the cross section. ffl Pileup correction: 0 % of the size of pileup correction is quoted as the pileup correction systematic uncertainty. he pileup correction is obtained from minimum bias data. he energy away from jets (electron) in dijet (W! eν) events, and the photon-jet balance in photon+jet events as a function of the number of reconstructed primary vertices were also measured. he quoted uncertainty covers variations from all of these cross-check studies. It results in less than % uncertainty in the cross section measurement. ffl Luminosity: 6 % uncertainty in normalization [4]. ffl Hadron to parton level correction: he systematic uncertainty on the hadron to parton level correction is estimated from the difference in the predictions for this correction from HERWIG and PYHIA. HERWIG does not include multiple parton interactions (MPI) in its UE model, and instead relies on initial state radiation (ISR) and beam remnants to populate the UE. PYHIA includes MPI as well as the components included in HERWIG. PYHIA predicts a larger correction at low. We conservatively take the difference between HERWIG and PYHIA for this systematic uncertainty (see figure 5). 8 VI. HEOREICAL PREDICIONS he prediction of pqcd was obtained from the next-to-leading order (NLO) program EKS [5] with CEQ6.M [] parton distribution functions (PDFs). he μ scale was chosen as the transverse momentum of the jet divided by two, which is the same as that used to determine the PDF. Using μ = P jet and P jet gives ο and 0 % smaller predictions in the cross section. Avalue of R sep =: [9]was used in the NLO calculation to mimic the splitting and merging step of the Midpoint algorithm when combining calorimeter towers, particles after hadronization, or partons after the parton shower. VII. RESULS he results are shown in figures 6 -. In each figure the inclusive differential jet cross section corrected to the hadron level is shown on the left, and the ratio of data corrected to the parton level to the NLO predictions of EKS is shown on the right. he yellow band shows the experimental systematic uncertainty while the blue band also includes the modeling uncertainty associated with the hadronization and underlying event corrections. here is an additional 6 % normalization uncertainty due to the uncertainty on the integrated luminosity which has not been included in the figures. he PDF uncertainty is drawn in red on the ratio plots [6]. he cross sections for the various rapidity regions are presented on figure where they have been scaled by different factors for presentation purposes. Figure shows the ratios to NLO pqcd predictions for the different rapidity regions. VIII. CONCLUSIONS A measurement was presented of the inclusive jet cross section for jets clustered by the CDF midpoint jet finding algorithm using over fb of data collected by the CDF experiment. Good agreement is seen in all rapidity regions with the pqcd predictions of the NLO program EKS using CEQ6.M parton distributions. In the most forward region (jy j > :6) the systematic uncertainty on the measurement is smaller than the PDF uncertaintywhich suggests that this measurement will lead to useful constraints on global PDF fits. Acknowledgments We thankthe Fermilab staff and the technical staffs of the participating institutions for their vital contributions. his workwas supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto
9 d σ dyd - - - -4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p /, R =. sep 0.< Y <0.7 - L=.04 fb Data / heory.5.5.5 Data corrected to the parton level Jet NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep - 0.< Y <0.7 L=.04 fb PDF Uncertainty on pqcd Data / NLO pqcd including hadronization and UE -7 0 0 00 00 400 500 600 700 0 0 00 00 400 500 600 700 FIG. 6: Measured inclusive jet cross section with the Midpoint algorithm in the region 0: < jy j < 0:7. he distribution for the hadron level cross section is shown on the left, while the ratio of data corrected to the parton level to the pqcd prediction ofeks is shown on the right. Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and echnology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A.P. Sloan Foundation; the Bundesministerium fuer Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK; the Russian Foundation for Basic Research; the Comision Interministerial de Ciencia y ecnologia, Spain; and in part by the European Community's Human Potential Programme under contract HPRN-C-000, and the Academy of Finland. [] E. Eichten, K. D. Lane, and M. E. Peskin, Phys. Rev. Lett. 50, 8 (98). [] D. Stump et al., JHEP, 046 (00), hep-ph/000. [] H. Fritzsch, M. Gell-Mann, and H. Leutwyler, Phys. Lett. B47, 65 (97). [4] D. J. Gross and F. Wilczek, Phys. Rev. D8, 6 (97). [5] J. Huston et al., Phys. Rev. D58, 404 (998), hep-ph/980444. [6] A. Affolder et al. (CDF), Phys. Rev. D64, 000 (00), hep-ph/0074. [7] A. Abulencia et al. (CDF Run II) (005), hep-ex/0500. [8] G. C. Blazey et al. (000), hep-ex/00050. [9] S. D. Ellis, J. Huston, and M. onnesmann, econf C060, P5 (00), hep-ph/044. [] A. Abulencia et al. (CDF II), Phys. Rev. Lett. 96, 00 (006), hep-ex/0506. [] F. Abe et al. (CDF), Nucl. Instr. Meth. A7, 87 (988). [] P.. Lukens (CDF IIb) (00), fermilab-m-98. [] B. L. Winer, Int. J. Mod. Phys. A6SC, 69 (00). [4]. Sjostrand et al., Comput. Phys. Commun. 5, 8 (00), hep-ph/0007. [5] G. Corcella et al., JHEP 0, 0 (00), hep-ph/006. [6] H. L. Lai et al. (CEQ), Eur. Phys. J. C, 75 (000), hep-ph/9908. [7] R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini (987), cern-dd/ee/84-. [8] G. Grindhammer, M. Rudowicz, and S. Peters, Nucl. Instrum. Meth. A90, 469 (990). [9] A. Bhatti et al. (005), hep-ex/05047. [0] P. Bagnaia et al. (UA), Phys. Lett. B44, 8 (984). [] B. Abbott et al. (D0), Phys. Rev. Lett. 86, 707 (00), hep-ex/006. [] R. Field (CDF) (00), fermilab ME/MC uning Workshop. [] R. Field and R. C. Group (CDF) (005), hep-ph/0598. [4] D. Acosta et al., Nucl. Instrum. Meth. A494, 57 (00). [5] S. D. Ellis, Z. Kunszt, and D. E. Soper, Phys. Rev. Lett. 64, (990). [6] J. Pumplin et al., Phys. Rev. D65, 040 (00), hep-ph/0. [7] We use a cylindrical coordinate system with the z coordinate along the proton beam direction and the origin at the
center ofthe detector, the azimuthal angle ffi, and the polar angle usually expressed through the pseudorapidity = ln tan( =). he rapidity y is defined as y = =ln((e + P z)=(e P z)) where E denotes the energy and P Z is the momentum component along z. he transverse energy and transverse momentum are given by: E = E sin( ) = P sin( ) wherep is the magnitude ofthe momentum vector. [8] he missing transverse energy (6 ~ E )isdefinedby, 6 ~ E = P i Ei ^n i,where^n i is a unit vector perpendicular to the beam axis and pointing at the i th calorimeter tower. Missing E significance is defined by, 6E f =6E =pp E. [9] he hadron level in the Monte Carlo generators is defined using all final-state particles with lifetime above s. [0] PYHIA-une A implies that the following parameters are set in PYHIA (CEQ5L): PARP(67)=4, MSP(8)=4, PARP(8)=, PARP(84)=0.4, PARP(85)=0.9, PARP(86)=0.95, PARP(89)=800, PARP(90)=. d σ dyd - - - -4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p /, R =. sep Y <0. - L=.04 fb Data / heory.5.5.5 Data corrected to the parton level Jet NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep - Y <0. L=.04 fb PDF Uncertainty on pqcd Data / NLO pqcd including hadronization and UE -7 0 0 00 00 400 500 600 700 0 0 00 00 400 500 600 700 FIG. 7: Measured inclusive jet cross section with the Midpoint algorithm in the region jy j < 0:. he distribution for the hadron level cross section is shown on the left, while the ratio of data corrected to the parton level to the pqcd prediction of EKS is shown on the right. d σ dyd - - - -4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p /, R =. sep 0.7< Y <. - L=.04 fb Data / heory.5.5.5 Data corrected to the parton level Jet NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep - 0.7< Y <. L=.04 fb PDF Uncertainty on pqcd Data / NLO pqcd including hadronization and UE -7 0 0 00 00 400 500 600 700 0 0 00 00 400 500 600 700 FIG. 8: Measured inclusive jet cross section with the Midpoint algorithm in the region 0:7 < jy j < :. he distribution for the hadron level cross section is shown on the left, while the ratio of data corrected to the parton level to the pqcd prediction ofeks is shown on the right.
d σ dyd - - - -4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p /, R =. sep.< Y <.6 - L=.04 fb Data / heory.5.5.5 Data corrected to the parton level Jet NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep -.< Y <.6 L=.04 fb PDF Uncertainty on pqcd Data / NLO pqcd including hadronization and UE -7 0 0 00 00 400 500 600 700 0 0 00 00 400 500 FIG. 9: Measured inclusive jet cross section with the Midpoint algorithm in the region : < jy j < :6. he distribution for the hadron level cross section is shown on the left, while the ratio of data corrected to the parton level to the pqcd prediction ofeks is shown on the right. d σ dyd - - - -4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p /, R =. sep.6< Y <. - L=.04 fb Data / heory.5.5.5 Data corrected to the parton level Jet NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep -.6< Y <. L=.04 fb PDF Uncertainty on pqcd Data / NLO pqcd including hadronization and UE -7 0 0 00 00 400 500 600 700 0 50 0 50 00 50 00 FIG. : Measured inclusive jet cross section with the Midpoint algorithm in the region :6 < jy j < :. he distribution for the hadron level cross section is shown on the left, while the ratio of data corrected to the parton level to the pqcd prediction ofeks is shown on the right.
d σ dyd 5 7 4 Data corrected to the hadron level NLO: EKS CEQ 6.M μ=p Midpoint R =0.7, f merge =0.75 cone /, R =. sep L=.04 fb - - 6 Y <0. (x ) 0.< Y <0.7 (x ) -8 - -4.6< Y <. (x ) -.< Y <.6 (x ) 0.7< Y <. 0 0 00 00 400 500 600 700 FIG. : Measured inclusive jet cross section at the hadron level with the Midpoint algorithm in the different rapidity regions. Data / heory Data / heory Data / heory.5.5.5.5.5.5.5 Y <0. 0.7< Y <..6< Y <..5.5 0 0 00 00 400 500 600 700 0.< Y <0.7.< Y <.6 0 00 00 400 500 600 700 PDF Uncertainty on pqcd Data (parton level) / NLO pqcd including hadronization and UE Midpoint R =0.7, f merge =0.75 cone NLO pqcd: EKS CEQ 6.M μ=p /, R =. sep L=.04 fb - FIG. : Ratio of the measured inclusive jet cross section at the parton level with the Midpoint algorithm to the pqcd prediction ofeks in the different rapidity regions.