Multiple Interactions

At this workshop, CDF presented preliminary results on the measurement of events where two scattering processes occur in the same event [20]. For distinct processes A and B, the cross section for this ``double parton (DP) scattering" is given by $\sigma_{\rm DP} = \sigma_A\sigma_B/\sigma_{\rm eff}$, where $\sigma_{\rm eff}$ is a process independent parameter.

Events were selected with a relatively low transverse energy (E_T> 16 GeV) ``photon" trigger in conjunction with three jets with E<sub>T</sub>> 5 GeV. The separation of DP events from the underlying QCD background is determined by studying variables sensitive to decorrelation effects. In particular, the azimuthal angle between the two best-balancing pairs (``photon"+jet versus dijet) is approximately flat for the DP signal and enables a statistical separation of events. A new feature of this analysis is that events with displaced vertices, where the jets are reconstructed from separate origins, are used to evaluate $\sigma_A\sigma_B$directly and hence reduce the theoretical uncertainties. This allows the first relatively precise determination of the effective cross section:

$$\sigma_{\rm eff}=(14.5\pm1.7^{+1.7}_{-2.3})~\rm{mb.}$$

No x-dependence is observed, within the uncertainty of $\simeq$ 20%. Assuming a uniformly dense ball of partons and using the measured inelastic $p\bar{p}$ cross section, one expects $\sigma_{\rm eff}=$11 mb. The measurement represents a milestone in the study of multiple interactions and provides the first significant experimental constraint on such processes.

Multiple interactions, where two or more partons interact in the same event, represent a considerable uncertainty in the analysis of photoproduction events at HERA. In particular, the extraction of the gluon content of the photon at relatively low $x_\gamma$ requires careful modelling of these interactions, since they can contribute up to 50% of the cross section at the relatively low E_T values (E_T>6 GeV) measured so far. The Tevatron result should aid in a realistic estimate of the uncertainties due to multiple interactions in the extraction of the gluon density of the photon at HERA. Similarly, such measurements improve background estimates to di-boson and boson+jet production at the Tevatron as well as the predictions of jet rates from multiple interactions at the LHC.