Measurement of the inclusive jet cross section in $p \bar{p}$ collisions at $\sqrt{s}=1.96 {\rm TeV}$

We report on a measurement of the inclusive jet cross section in $p \bar{p}$ collisions at a center-of-mass energy $\sqrt s=$1.96 TeV using data collected by the D0 experiment at the Fermilab Tevatron Collider corresponding to an integrated luminosity of 0.70 fb$^{-1}$. The data cover jet transverse momenta from 50 GeV to 600 GeV and jet rapidities in the range -2.4 to 2.4. Detailed studies of correlations between systematic uncertainties in transverse momentum and rapidity are presented, and the cross section measurements are found to be in good agreement with next-to-leading order QCD calculations.

(Dated: August 12, 2008) We report on a measurement of the inclusive jet cross section in pp collisions at a center-of-mass energy √ s =1.96 TeV using data collected by the D0 experiment at the Fermilab Tevatron Collider corresponding to an integrated luminosity of 0.70 fb −1 .The data cover jet transverse momenta from 50 GeV to 600 GeV and jet rapidities in the range -2.4 to 2.4.Detailed studies of correlations between systematic uncertainties in transverse momentum and rapidity are presented, and the cross section measurements are found to be in good agreement with next-to-leading order QCD calculations.
PACS numbers: 13.87.Ce,12.38.Qk The measurement of the cross section for the inclusive production of jets in hadron collisions provides stringent tests of quantum chromodynamics (QCD).When the transverse momentum (p T ) of the jet with respect to the beam axis is large, contributions from long-distance processes are small and the production of jets can be calculated in perturbative QCD (pQCD).The inclusive jet cross section in pp collisions at large p T provides one of the most direct probes of physics at small distances.In particular, it is directly sensitive to the strong coupling constant (α s ) and the parton distribution functions (PDFs) of the proton.Additionally, it can be used to set constraints on the internal structure of quarks [1].Deviations from pQCD predictions at large p T can indicate new physical phenomena not described by the standard model of particle physics.A measurement over the widest possible rapidity range provides simultaneous sensitivity to the PDFs as well as new phenomena expected to populate mainly low rapidities.These data will have a strong impact on physics at the CERN Large Hadron Collider (LHC) where searches for new particles and higher dimensions suffer from poor knowledge of PDFs [2].
In this Letter, we report on a measurement from the D0 experiment of the inclusive jet cross section in pp collisions at a center-of-mass of √ s = 1.96TeV.The data sample, collected with the D0 detector during 2004-2005 in Run II of the Fermilab Tevatron Collider, corresponds to an integrated luminosity of L = 0.70 fb −1 [3].The increased pp center-of-mass energy between Run I ( √ s = 1.8 TeV) and Run II leads to significant increase in the cross section at large p T -a factor of three at p T ∼ 550 GeV.The cross section is presented in six bins of jet rapidity (y), extending out to |y| = 2.4, as a function of jet p T starting at p T = 50 GeV, and provides the largest data set of the inclusive jet spectra at the Tevatron with the smallest experimental uncertainties to date.The measurement also extends earlier inclusive jet cross section measurements by the CDF and D0 collaborations [4,5] and improves the systematic uncertainties compared to previous measurements by up to a factor of two over a range of rapidity up to 2.4 at high p T .The primary tool for jet detection is the finely segmented liquid-argon and uranium calorimeter that has almost complete solid angular coverage [6].The central calorimeter (CC) covers the pseudorapidity region |η| < 1.1 and the two endcap calorimeters (EC) extend the coverage up to |η| ∼ 4.2.The intercryostat region (ICR) between the CC and EC contains scintillator-based detectors that supplement the coverage of the calorimeter.The Run II iterative seed-based cone jet algorithm including mid-points [7] with cone radius R = (∆y) 2 + (∆φ) 2 = 0.7 in rapidity y and azimuthal angle φ is used to cluster energies deposited in calorime-ter towers.The same algorithm is used for partons in the pQCD calculations.The binning in jet p T is commensurate with the measured p T resolution.
Events are required to satisfy jet trigger requirements.Only jets above a given p T threshold are kept by the highest level trigger (L3).The cross section is corrected for jet trigger inefficiencies (always below 2%) determined using an independent sample of muon triggered events.
The jet p T is corrected for the energy response of the calorimeter, energy showering in and out the jet cone, and additional energy from event pile-up and multiple proton interactions.After applying these corrections, the jet four momentum is given at the particle level, which means that they represent the real energy of the jet made out of the stable particles resulting from the hadronization process following the hard pp interaction..The electromagnetic part of the calorimeter is calibrated using Z → e + e − events [8].The jet response for the region |η| < 0.4 is determined using the momentum imbalance in γ+jet events.The p T imbalance in dijet events with one jet in |η| < 0.4 and the other anywhere in η is used to intercalibrate the jet response in η, as a function of jet p T .Jet energy scale corrections are typically ∼50% (20%) of the jet energy at 50 (400) GeV.Further corrections due to the difference in response between quark-and gluoninitiated jets are computed using the pythia [9] event generator, passed through a geant-based [11] simulation of the detector response.These corrections amount to ∼ +4% at jet energies of 50 GeV and ∼ −2% at 400 GeV in the CC.The relative uncertainty of the jet p T calibration ranges from 1.2% at p T ∼ 150 GeV to 1.5% at 500 GeV in the CC, and 1.5-2% in the ICR and EC .
The position of the pp interaction is reconstructed using a tracking system consisting of silicon microstrip detectors and scintillating fibers located inside a solenoidal magnetic field of 2 T [6].The position of the vertex along the beamline is required to be within 50 cm of the detector center.The signal efficiency of this requirement is 93.0 ± 0.5%.A requirement is placed on the missing transverse energy in the event, computed as the transverse component of the vector sum of the momenta in calorimeter cells, to suppress the cosmic ray background and is > 99.5% efficient for signal.Requirements on characteristics of shower development are used to remove the remaining background due to electrons, photons, and detector noise that mimic jets.The efficiency for these requirements is > 99% (> 97.5% in the ICR).After all these requirements, the background is < 0.1% in our sample.
The D0 detector simulation provides a good description of jet properties including characteristics of the shower development.The correction to the jet cross section for muons and neutrinos, not reconstructed within jets, is determined using pythia and is 2%, independent of p T and y.The corrections for jet migration between bins in p T and y due to finite resolution in energy and position are determined in an unfolding procedure, based on the experimental p T and y resolutions.The jet p T resolution is obtained using the p T imbalance in dijet events and is found to decrease from 13% at p T ∼ 50 GeV to 7% at p T ∼ 400 GeV in both the CC and the EC.The resolution in the ICR is 16% at p T ∼ 50 GeV decreasing to 11% at p T ∼ 400 GeV.The method to unfold the data uses a four-parameter ansatz function [10] to parametrize the p T dependence of the jet cross section convoluted with the measured p T resolution and fitted to the experimental data.
The unfolding corrections vary between 20% at a jet p T ∼ 50 GeV and 40% at 400 GeV in the CC.In the EC and the ICR, the corrections are less than 20% at p T ∼ 50 GeV, but increase to 80% at the largest p T and y.Bin sizes in p T and y are chosen to minimize migration corrections due to the experimental resolution.The y resolution is better than 0.05 (0.01) for jets with p T ∼ 50 GeV (400 GeV), and leads to a migration correction less than 2% in most bins, and 10% in the highest y bin.
The results of the inclusive jet cross section measurement corrected to the particle level are displayed in Fig. 1 in six |y| bins as a function of p T .The cross section extends over more than eight orders of magnitude from p T = 50 GeV to p T > 600 GeV.Perturbative QCD predictions to next-to-leading order (NLO) in α S , computed using the fastNLO program [12] (based on nlo-jet++ [13]) and the PDFs from CTEQ6.5M [14], are compared to the data.The renormalization and factorization scales (µ R and µ F ) are set to the individual jet p T .The theoretical uncertainty, determined by changing µ R and µ F between p T /2 and 2p T , is of the order of 10% in all bins.The predictions are corrected for non-perturbative contributions due to the underlying event and hadronization computed by pythia with the CTEQ6.5MPDFs, the QW tune [15], and the two-loop formula for α S .These non-perturbative corrections to theory extend from +10% to +20% at p T ∼ 50 GeV between |y| < 0.4 and 2.0 < |y| < 2.4.The corrections are of order +5% for p T ∼ 100 GeV, and smaller than +2% above 200 GeV.
The ratio of the data to the theory is shown in Fig. 2. The dashed lines show the uncertainties due to the different PDFs coming from the CTEQ6.5 parametrizations.The predictions from MRST2004 [16] are displayed by the large dashed line.In all y regions, the predictions agree well with the data.There is a tendency for the data to be lower than the central CTEQ prediction -particularly at very large p T -but they lie mostly within the CTEQ PDF uncertainty band.The p T dependence of the data is well reproduced by the MRST parametrization whose systematic uncertainty is slightly smaller than that from the CTEQ parametrization.The experimental systematic uncertainty is comparable to the PDF uncertainties.The theoretical scale uncertainty, obtained by varying the factorization and renormalization scales between µ R = µ F = p T /2 and µ R = µ F = 2p T , is typically 10-15%.In most bins, the experimental uncertainties are of the same order as the theoretical uncertainties.Tables of the cross sections together with their uncertainties are given in Ref. [17].
Correlations between systematic uncertainties are studied in detail to increase the value of these data in future PDF fits [17] and their impact on LHC physics in particular.Point-to-point correlations in p T and y are provided for the 24 sources of systematic uncertainty.The relative uncertainties in percent on the cross section measurement are shown in Fig. 3 for the five most significant sources of systematic uncertainty in |y| < 0.4 and 2.0 < |y| < 2.4.The luminosity uncertainty of 6.1%, fully correlated in p T and y, is not displayed in Fig. 3.The other y bins have similar correlations in shape and values between these two extreme bins.The total uncorrelated uncertainty is < 3% in the CC, and < 15% in the EC.
The two largest systematic uncertainties are due to the electromagnetic energy scale obtained from Z → e + e − events [8], and the photon energy scale in the CC obtained using the difference in the calorimeter response between photons and electrons in the detector simulation.The uncertainty on the photon energy scale is mainly due to the limited knowledge of the amount of dead material in front of the calorimeter and from the physics modeling of electromagnetic showers in the geant-based [11] simulation.These two contributions to the jet cross section uncertainty are ∼ 5% in the CC and 5 − 15% in the EC.The large-p T extrapolation of jet energy scale is determined using the detector simulation with the singlepion response tuned to γ+jet data.The uncertainty rises to 12% (30%) in the CC (EC), and is dominated by the uncertainty in the jet fragmentation, estimated by comparing the fragmentation models in pythia and herwig [18].The uncertainty in η intercalibration corresponds to systematic uncertainties associated with the procedure to equalize the calorimeter response in different regions of η in dijet events.These systematic uncertainties are negligible in the CC because the η dependent response is calibrated with respect to the CC, but extend up to 25% in the EC.Finally, systematic uncertainties associated with showering effects, due primarily to the modeling of the hadronic shower development in the detector and differences between pythia and herwig, range from 3% at low p T to 7% (15%) at large p T in the CC (EC).
To show the potential impact of using point-to-point uncertainty correlations in jet p T and y on PDF determination, we give in Fig. 3 the uncorrelated and total systematic uncertainties as a function of jet p T as a percentage of the jet cross section measurement.The total uncorrelated uncertainties are less than 15% and 25% of the full uncertainties in the CC and EC respectively.The full systematic uncertainties are similar in size to the PDF uncertainties (Fig. 2) and the detailed analysis of the correlations which have been performed will make it possible to further constrain the PDFs.Knowledge of these correlations is especially important for constraining the PDFs in NNLO pQCD fits where the uncertainties due to the dependence on the choice of the renormalization and factorization scales are smaller.The point-topoint correlations for the 24 different sources of systematic uncertainties are given in Ref. [17].
In conclusion, the measured inclusive jet cross section corrected for experimental effects to the particle level in pp collisions at √ s = 1.96TeV with L = 0.70 fb −1 is presented for six |y| bins as a function of jet p T , substantially extending the kinematic reach and improving the precision of existing inclusive jet measurements.NLO pQCD calculations with CTEQ6.5M or MRST2004 PDFs agree with the data and favor the lower edge of the CTEQ6.5 PDF uncertainty band at large p T and the shape of the p T dependence for MRST2004.A full analysis of correlations between sources of systematic uncertainty is performed, increasing the potential impact of these data in global PDF fits and on new phenomena searches at the LHC. and the Alexander von Humboldt Foundation.

FIG. 2 :
FIG.2: Measured data divided by theory for the inclusive jet cross section as a function of jet pT in six |y| bins.The data systematic uncertainties are displayed by the full shaded band.NLO pQCD calculations, with renormalization and factorization scales set to jet pT using the CTEQ6.5MPDFs and including non-perturbative corrections, are compared to the data.The CTEQ6.5 PDF uncertainties are shown as small dashed lines and the predictions with MRST2004 PDFs as large dashed lines.The theoretical scale uncertainty, obtained by varying the factorization and renormalization scales between µR = µF = pT /2 and µR = µF = 2pT , is typically 10-15%