A Brief Summary of QCD Results at CDF

The highest Et jets recorded by CDF are the result of interactions at distance scales of a few times 10^-17 cm, almost an order of magnitude smaller than the weak scale ! The inclusive jet cross-section has been measured from jet transverse energies of 15 GeV up to in excess of 400 GeV, a range over which the cross-section falls by 9 orders of magnitude ! Current NLO perturbative QCD predictions give an excellent description of this spectrum except that they slightly (but significantly) underestimate the observed rate in the region Et > 200 GeV. The origin of the discrepancy is not yet understood, but might indicate an inadequacy of the current QCD calculations (e.g. an inadequate gluon distribution function at high x) and this is under study. The spectrum of two-jet masses and the spectrum of total-Et (summed over all jet Ets in each event) also exhibit small deviations from the current QCD predictions at the highest masses and total-Et. The two-jet angular distribution is however consistent with the NLO QCD expectations, and has been used to place a limit on the scale of quark substructure, Lambda > 1.4 TeV. The detailed kinematic properties of multijet events (with up to 6 jets) at the highest multijet masses have also been shown to be fully consistent with QCD expectations.

Due to the evolution of alpha_s and the evolution of parton distributions, QCD predicts scaling violations; i.e. if the invariant jet cross-section is plotted as a function of the dimensionless variable xT = 2 Et / sqrt(s) then the result depends on sqrt(s). In the 1989 data run CDF collected data at sqrt(s) = 546 GeV, and compared the invariant jet cross-section at 546 GeV and 1800 GeV. Scaling violation was observed, but at low Xt the violations were at a level smaller than the NLO QCD predictions. CDF have therefore recently taken a much larger sample of low energy data, this time at sqrt(s) = 630 GeV. Preliminary results confirm the sqrt(s) = 546 GeV observations, but the full systematics have not yet been evaluated.

The W + n-jet and Z + n-jet cross sections and associated jet production properties have been measured for n=1 to 4. The data consist of 6708 Z -> e+e- decays and 50387 W -> e nu decays from 106 pb**-1 of integrated luminosity. About 20% of the W and Z events have associated jets with Et > 15 GeV. These data are corrected for QCD backgrounds, and the contribution from Standard Model top predictions subtracted from the W+jets events. The resulting jet production properties are compared to QCD predictions for jets radiated from direct W/Z production. The jet rates and properties are quite well described by LO QCD predictions if the LO cross section is scaled by 1.7 (using a QCD renormalization scale of Q**2 = M**2 + Pt**2 of the boson).

The inclusive direct photon spectrum has been compared to NLO QCD predictions. A long-standing problem has been that the predictions do not give a good description of the shape of the observed spectrum. This has motivated improved calculations which have reduced but not eliminated the discrepancy. Recent developments suggest that if additional (parton shower) gluon radiation is added to the NLO QCD model then a good agreement is obtained. This presence of this additional gluon radiation also broadens the pT spectrum for diphotons, and this has been observed. The need for additional gluon radiation has broad implications outside of CDF for the analysis of lower energy direct photon data and extraction of parton distribution functions. The photon + jet rapidity distribution, and the photon + 1-jet and photon + 2-jet angular distributions have also been measured and compared with QCD predictions. The measured photon + 1-jet angular distribution, which is very sensitive to photon fragmentation effects, is observed to be steeper than the NLO QCD, perhaps indicating a larger fragmentation contribution than is presently in the calculation.

In PRL 70, 713 (1993) CDF showed that the Et dependent shapes of jets (the amount of energy contained in a cone as a function of cone size) is qualitatively reproduced by NLO QCD calculations and by QCD parton shower Monte Carlo predictions. Quantitatively, the measured shapes lie between the NLO and the parton shower Monte Carlo predictions, and the conclusion is that the radiation of a single hard gluon in the final state accounts for much of the observed jet shape, although it is clearly not the full story. More recently, CDF has measured the Et dependent fragmentation function for charged tracks and compared with MLLA QCD predictions. There is very impressive agreement between the observed and predicted fragmentation functions. The QCD model has 2 parameters, which are the cutoff scale at which partons turn themselves into hadrons, and a normalization parameter which specifies how many charged particles each parton gives rise to. It is found that the cutoff scale is 230+/-20 MeV. The fragmentation fits agree with equivalent results from TASSO/OPAL/ALEPH, but the jet Et range probed is much larger than for the e+e- experiments. Finally, CDF has also used tracking to study subclusters within jets. Evidence for subclusters in high-Et jets is observed, and subcluster properties have been compared with HERWIG parton shower Monte Carlo predictions. In the Monte Carlo subclusters arise due to color preconfinement. In general HERWIG gives a good description of many of the subcluster properties, a more detailed analysis is in progress.

CDF has made many heavy flavor (b and c) production measurements, including J/psi, psi(2S), and b production (PRL 69, 3704 (1993), PRL 71, 500 (1993)), and more recently the b and c content in high-Et jets and charm production in lepton + photon events or events tagged by a D*. The level of agreement/disagreement between observed rates and QCD predictions varies from channel to channel. CDFs measurements of heavy flavor production seem to be providing a challenge to the current QCD calculations.

The double parton scattering (DPS) cross-section was reported by CDF in PRD 47, 4857 (1993) for events in which both scatters result in two jets with Et > 25 GeV. About 5% of the data sample was observed to come from DPS. More recently CDF has observed DPS in the photon + 3-jet channel (one scatter -> two-jets, and the other -> photon + jet). In this data sample roughly 50% of the events come from DPS, enabling the detailed properties of DPS events to be studied. No evidence of significant correlations between the two scatters is observed.

First evidence for the observation of a separate population of jet events in which the jets are separated by a rapidity gap (containing an absense of activity) was reported by CDF in PRL 74, 855 (1995). More recently, data was taken using the roman-pot trigger during 1800 GeV running at low-luminosity (10E29). The inclusive roman-pot data show characteristics of diffractive events, i.e. rapidity-gaps, boosted center-of-mass systems, correlations between both eta-max and calorimeter mass, and the fraction of antiproton momentum loss $\xi$. The dijet candidates have a cross-section of 0.64 $\mu$b, and display the same characteristics. Diffractive W production has also been observed. Further studies to determine the pomeron structure are in progress.