High-E_T Jet Results from the Tevatron

The Tevatron Collider provides a unique opportunity to study the properties of hard interactions in $p\overline{p}$ collisions at short distances. The production of jets at large E_T and its comparison with perturbative QCD calculations are of interest as they can serve as a test of the elementarity of the partons.

The CDF and DØ collaborations have measured jet cross sections over ten orders of magnitude in $d^2\sigma/dE_Td\eta$ up to E_T = 500 GeV, half way to the kinematic limit. The challenge of measuring such a steeply falling spectrum is the understanding of the energy calibration of jets. The highest E_T jets are not directly calibrated, resulting in large uncertainties. In this kinematic region the NLO calculations are well understood at the 10-20% level. However, precise knowledge of the parton distribution functions in the proton is required before firm conclusions can be drawn from the comparison of data and theory. Collider data can constrain the parton distribution functions in the proton and especially the gluon distribution at moderate x. Kosower presented a formalism to make such an extraction possible using NLO calculations, while minimising the amount of numerical computation involved [26].

The preliminary (published) inclusive jet cross sections as measured by CDF using the 1994-1995 (1992-1993) data sample in the pseudorapidity region of $0.1\leq\vert\eta\vert\leq0.7$ are compared to the NLO QCD in Fig. 5(a) [27,28]. The latter are based on calculations by EKS [29] with CTEQ3M [30] parton densities, renormalisation and factorisation scales $\mu=E_T^{\rm jet}/2$, and the standard Snowmass jet cone algorithm. The data and the prediction are in excellent agreement for E_T < 250 GeV; at higher E_T, however, the data lie significantly above the predictions.

  

Figure: Ratio between experiment and theory for the inclusive jet cross section as measured by CDF and DØ.

DØ presented updated inclusive jet cross sections in the region of $\vert\eta\vert\leq0.5$ with significantly reduced systematic uncertainties (by about a factor of two), coming from a re-evaluation of the jet energy scale corrections [27]. As shown in Fig. 5(b), these results are in excellent agreement with NLO QCD over the entire E_T range. DØ compares the data to NLO QCD predictions using JETRAD [31], the CTEQ3M parton densities, the renormalisation and factorisation scales $\mu=E_T^{\rm max}/2$, and a modified Snowmass jet cone algorithm with $R_{\rm sep}$=1.3.

It should be noted that the DØ and CDF data have been compared to NLO QCD with slightly different input parameters which can introduce an E_T-dependent variation of $\simeq~10\%$ on the theoretical predictions [27]. Also the two measurements probe different $\eta$ regions.

In order to compare directly the results of the two experiments, DØ also performed the analysis in the CDF $\eta$ region. Figure 6 shows the CDF data points as compared to a fit of the DØ data in the $0.1\leq\vert\eta\vert\leq0.7$ region. The error band corresponds to the DØ systematic error which is mainly due to the jet energy scale uncertainty. The CDF data lie above the DØ fit but are within the experimental uncertainties. For a more quantitative comparison between the two experiments, the correlations in the systematic uncertainties of the two data sets must be taken into account.

  

Figure: Residual plot of the CDF data with a fit on the $0.1\leq\vert\eta\vert\leq0.7$ DØ data. The band shown represents the DØ systematic uncertainty.

The dijet angular distribution is an ideal tool to determine whether any possible excess of events in high-E_T inclusive jet production is due to new physics effects. The angular distribution of the outgoing partons is strictly governed by the helicities of the partons participating in the hard process and is relatively insensitive to the parton densities. Any unusual contact interaction (with effective scale $\Lambda$) will flatten the centre of mass scattering angle distribution (or create an excess of events at low $\chi$). The CDF published results on dijet angular distributions give a lower limit of $\Lambda \gt 1.8$ TeV. Figure 7 shows the recent DØ $\chi$ distributions which are in good agreement with NLO QCD [27]. Using these data, DØ rules out at 95% CL a model where quarks couple with a universal contact interaction of scale $\Lambda\sim 2.1$ TeV.

  

Figure: Dijet angular distributions for DØ data compared to JETRAD for LO and NLO predictions with two different renormalisation/factorisation scales.