Diffraction at the Tevatron

The study of diffraction benefits by looking at information from other types of interaction. In e⁺e^- where there is no complex colour state in the interacting beams, various searches for rapidity gaps yield results which can be explained in terms of exponentially-suppressed colour exchange and these data do not require the introduction of a ``pomeron" [35]. In contrast, the earliest work on diffractive processes focussed on pp collisions where two complex colour states interact. The latest studies at the Tevatron complement those at HERA and allow tests of factorisation in ep compared to $\bar{p}p$.

The studies of colour singlet exchange between jets at HERA was inspired by earlier studies at the Tevatron. These studies determined percentage gap-fractions of $1.07\pm 0.10^{+0.25}_{-0.13}$% for DØ [36] and $0.86\pm0.12$% for CDF [37]. The behaviour of this colour singlet fraction as a function of average dijet energy is shown in Fig. 30(a) for jet E_T^jet thresholds of 15 GeV (low), 25 GeV (medium) and 30 GeV (high) [38]. In Fig. 30(b), the gap-fraction is examined as a function of $\Delta\eta$. A simple two-gluon exchange model with no additional QCD dynamics would tend to produce a flat gap-fraction, but the tendency towards an increasing gap-fraction with $\Delta\eta$ indicates an additional dynamical mechanism is necessary to describe the data. The differences in the overall gap-fractions observed at HERA near 10%, compared to those at Fermilab of approximately 1%, may reflect the higher W values of the Tevatron compared to HERA. But the fact that this difference is so large indicates differences in the underlying high-$x_\gamma$ $\gamma p$ interactions compared to the relatively low-x $p\bar{p}$ interactions where spectator interactions are more likely to fill in the gap.

  

Figure 30: Percentage gap-fraction, f_s, as a function of (a) the average dijet E_T^jet and (b) the rapidity gap between the two jets for the high E_T^jet jet sample.

Diffractive dijet production has been studied at the Tevatron. The presence of a diffracted proton may be identified either by a large rapidity gap on either the proton or antiproton side or by directly detecting the leading proton (CDF roman pots). In the rapidity gap analyses, DØ measure uncorrected dijet rates with E_T^jet > 12 GeV and $\vert\eta_{jet}\vert > 1.6$ in coincidence with the multiplicity in the electromagnetic calorimeter ( $2.0 < \vert\eta\vert < 4.1$) opposite the dijet system, as shown in Fig. 31(a). Similarly, CDF measure the multiplicity in the forward part of the calorimeter ( $2.4 < \vert\eta\vert < 4.2$) in coincidence with the number of hits in the BBC scintillator counter close to the beampipe ( $3.2 < \vert\eta\vert < 5.9$), as shown in Fig. 31(b). Here the jets are measured for E_T^jet > 20 GeV and $1.8 < \vert\eta_{jet}\vert < 3.5$ the diffractive events concentrate in the region $0.005 < \xi < 0.015$. The ratio of diffractive dijet events is measured by CDF to be $R_{GJJ} = 0.75 \pm 0.05 \pm 0.09$% and by DØ to be $R_{GJJ} = 0.67 \pm 0.05$%. These preliminary figures are therefore in good agreement and can be used to constrain the gluon content of the pomeron. In addition, $R_{\bar{p}JJ} = 0.109 \pm 0.003 \pm 0.016$% has been measured using the CDF roman pots in region of large $\xi$ ( $0.05 < \xi < 0.1$, E_T^jet > 10 GeV and |t| < 1 GeV²). This is a region where reggeon (quark-like) contributions are presumably important.

  

Figure: (a) Multiplicity opposite the dijet system measured in the DØ  electromagnetic calorimeter compared to negative binomial fits used to estimate the non-diffractive contribution. (b) Forward calorimater tower multiplicity versus number of hits in the BBC scintillator counter; the diffractive peak corresponds to no hits in either detector.

CDF have also tagged diffractive W production using high-p_T electrons/positrons and missing p_T to tag the W and then searching for a rapidity gap on the opposite side as in the dijet gap analysis [39]. The corrected ratio for diffractive/non-diffractive W-production is measured to be

$$R_W = 1.15 \pm 0.51 \pm 0.20 \%.$$

An important question when relating the various diffractive measurements which involve a hard scale is whether Regge factorisation, in terms of a pomeron flux and parton densities within the pomeron, is applicable. In particular, if this approach is to be useful, a universal flux is required (or a QCD description of the non-universal correction to the flux). In this context, the rates for diffractive processes at HERA are compared to those observed at the Tevatron below.

We have two sets of CDF data probing the pomeron structure at similar momentum scales, E_T^jet and M_W. Each probes the large z structure of the pomeron with the dijet and W data predominantly sampling the (hard) gluon and quark distributions, respectively. In addition, we have the corresponding DIS [22] and jet HERA data sampling the (hard) gluon and quark distributions, respectively. In Fig. 32 the momentum fraction carried by the (hard) gluon, c_g, is plotted versus the momentum fraction of partons in the pomeron assuming a Donnachie-Landshoff flux. The CDF data are consistent with a momentum fraction carried by the gluons of $c_g = 0.7\pm 0.2$, in agreement with the ZEUS measurements of $c_g \sim 0.55 \pm 0.25$, taking into account the systematic uncertainties due (mainly) to the estimation of the non-diffractive background. This in turn can be compared with the H1 NLO parton distributions (see Fig. 26) which indicate $c_g \simeq 0.8$ in the high Q² region. There is therefore reasonable agreement on the parton content of the pomeron. However, the overall diffractive rates are significantly higher at HERA compared to the Tevatron. This is reflected in the difference in the overall level of the ZEUS and CDF data in Fig. 32. This corresponds to a significantly different flux of pomerons (i.e. breaking of Regge factorisation) which has been predicted in terms of QCD [40,41] to reduce the diffractive cross-sections for processes which have two strongly-interacting initial state hadrons. These effects are not apparent in the HERA data, where a virtual photon or a (predominantly) direct photon participate in the hard scattering process.

  

Figure 32: Momentum fraction of hard partons in the pomeron assuming a Donnachie-Landshoff flux versus the momentum fraction carried by the gluons in the pomeron. The ZEUS band corresponds to the allowed region using the fits to the DIS and jet data (statistical errors only). The shaded band corresponds to the allowed region from the CDF dijet and W analysis. The constraints given by the earlier UA8 jet data are also indicated.

Double pomeron exchange, where the p and $\bar{p}$ remain intact, has also been studied by CDF and DØ for their dijet samples. This process should be directly sensitive to Regge-factorisation breaking effects. Both experiments find a ratio of hard double pomeron exchange events to non-diffractive events of $\simeq 10^{-6}$. This is consistent with independent dissociation of the p and $\bar{p}$, with probabilities $\simeq 10^{-3}$, but further studies are required to establish these rates and determine whether these can be explained by the factorisation-breaking calculations [41].