Comparison of three-jet events in $p\overline{p}$ collisions at $\sqrt{s}=1.8$ TeV to predictions from a next-to-leading order QCD calculation

The properties of three-jet events with total transverse energy greater than 320 GeV and individual jet energy greater than 20 GeV have been analyzed and compared to absolute predictions from a next-to-leading order (NLO) perturbative QCD calculation. These data, of integrated luminosity $86{\mathrm{p}\mathrm{b}}^{-1}$, were recorded by the CDF Experiment for $p\overline{p}$ collisions at $\sqrt{s}=1.8$ TeV. This study tests a model of higher order QCD processes that result in gluon emission and may give some indication of the magnitude of the contribution of processes higher than NLO. The total cross section is measured to be $466\pm 3(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}.{)}_{-70}^{+207}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}.)$ pb. The differential cross section is furthermore measured for all kinematically accessible regions of the Dalitz plane, including those for which the theoretical prediction is unreliable. While the measured cross section is consistent with the theoretical prediction in magnitude, the two differ somewhat in shape in the Dalitz plane.

Figure 1

The three-jet data, after all selection requirements have been applied. The energy correction procedure (see text) has not been applied. The figures at the corners of the distribution represent typical three-jet topologies in those regions of the Dalitz plane.

Figure 2

The event density in the Dalitz plane for (a) the data and for (b) the prediction by the NLO Monte Carlo calculation with CTEQ4M, normalized to luminosity.

Figure 3

The fractional difference between the data and the theoretical prediction, using CTEQ4M, as a function of $X_4$, averaged over $X_3$. The vertical bands show the systematic uncertainties. The error bars show the statistical uncertainties in cases where those are larger than the size of the symbol used. The prediction is normalized to the data to facilitate a comparison of the shapes of the distributions.

Figure 4

The fractional difference between corrected data and the NLO prediction, using the CTEQ4M parton distribution function, as a function of $X_3$ for various $X_4$ bins. Error bars reflect statistical uncertainty for cases in which it is larger than the size of the symbol used. Shaded bands indicate systematic uncertainty. The prediction is normalized to the luminosity of the data.