Central Rapidity Gaps  

The results discussed in this section have been published in [1]. We have isolated a sample of hard photoproduction events containing at least two jets of transverse energy E_T^jet > 6 GeV. The jets are found using a cone algorithm with jet cones of radius 1 in $\eta - \varphi$ space. The pseudorapidity interval between the jet centres, $\Delta\eta$, exceeds 3.5 in 535 of the 8393 events. Note that to leading order $\Delta\eta = \ln (\hat{s} / -\hat{t})$ where $\hat{s}$ and $\hat{t}$ are the usual Mandelstam variables of the hard subprocesses. $\Delta\eta \gt 3.5$ therefore means that $\hat{s} \gt 30 \cdot - \hat{t}$ which falls into the Regge regime, $\hat{s} \gg - \hat{t}$.

Gap candidate events are defined as those which have no particles of E_T^particle > 300 MeV between the edges of the jet cones in pseudorapidity. The size of the gap therefore lies between $\Delta\eta$ and $\Delta\eta -2R = \Delta\eta -2$.

An event from this sample is shown in Figure 5.

 

Figure:   A hard photoproduction event with a central gap in the ZEUS detector. The z-R view of the ZEUS detector is shown on the left side. The lego plot of the E_T weighted energy deposits in the calorimeter versus their $\eta$ and $\varphi$ is shown in the upper right picture and the lower right picture shows the x-y cross section through the ZEUS detector.

There are two high transverse energy jets in this event which are back to back in $\varphi$ and have a pseudorapidity interval of $\Delta\eta = 3.6$.There are additional energy deposits around the forward beam pipe which correspond to the proton remnant and energy deposits near the rear beam pipe which may be associated with the photon remnant. This is in fact a gap candidate event. There are no candidate particles in the pseudrapidity interval between the jet cones having a transverse energy of E_T^particle > 300 MeV. There are, however, some very low energy energy deposits in this region which could in some cases be due to calorimeter noise. Alternatively they may be particles which are so soft that they have no memory of their parent parton's direction. The E_T^particle threshold is a necessary theoretical tool [5,6,7] as well as a convenient experimental cut.

The characteristics of this event sample are illustrated in Figure 6. Here the data are shown uncorrected for any detector effects, as black dots. The errors shown are statistical only. The data are compared to predictions from the PYTHIA [8,9] generator for hard photoproduction processes. These predictions have been passed through a detailed simulation of the selection criteria and of the detector acceptance and smearing.

 

Figure:   Sample characteristics. Errors are statistical only. No correction for detector effects has been performed. Monte Carlo simulated events have been subjected to full detector simulation. (a) Jet profile. Data are shown as black dots and PYTHIA standard hard photoproduction processes are shown as the solid line. (b) The $\Delta\eta$ distribution. Data are shown as black dots, the PYTHIA standard sample is shown by the open circles and the PYTHIA sample containing 10% of photon exchange processes is shown by the stars.

Figure 6(a) shows the average profile of the two highest E_T^jet jets. In the jet profile, $\delta\eta^{cell} = \eta^{cell} - \eta^{jet}$ of each calorimeter cell is plotted, weighted by the cell transverse energy, for cells with $\vert\varphi^{cell} - \varphi^{jet}\vert$ less than one radian. The data show good collimation and a jet pedestal which increases gradually towards the forward direction. The PYTHIA prediction for the standard direct and resolved hard photoproduction processes is shown by the solid line for comparison. The description is reasonable, however there is a slight overestimation of the amount of energy in the jet core and underestimation of the jet pedestal. Higher order processes and secondary interactions between photon and proton spectator particles are neglected in this Monte Carlo simulation. It is anticipated that their inclusion could bring the prediction into agreement with the data [10,11]. Notice that, naïvely, this discrepancy would be expected to give rise to proportionally fewer events containing a rapidity gap in the data than in the Monte Carlo sample.

Figure 6(b) shows the magnitude of the pseudorapidity interval between the two highest transverse energy jets, $\Delta\eta$. The number of events is rapidly falling with $\Delta\eta$ but we still have a sizeable sample of events with a large value of $\Delta\eta$.This distribution is well described by the standard PYTHIA simulation of photoproduction events which is here represented by open circles. The stars show a special PYTHIA sample which has been introduced in this analysis primarily for the purpose of obtaining a good description of the data and understanding detector effects. 90% of this sample is due to the standard photoproduction processes. The other 10% of this sample is due to quark-quark scattering via photon exchange (Figure 3(a) with the $I\!\!P$ replaced by a $\gamma$) and obviously this 10% contains no contribution from leading order direct photoproduction processes. (Note that 10% is about two orders of magnitude higher than one would obtain from the ratio of the electroweak to QCD cross sections.) The combined Monte Carlo sample also provides a good description of the $\Delta\eta$ distribution.

We define the gap-fraction, $f(\Delta\eta)$, to be the fraction of dijet events which have no particle of E_T^particle > 300 MeV in the rapidity interval between the edges of the two jet cones. The gap-fraction, uncorrected for detector effects, is shown in Figure 7. The data are shown as black dots, the events from the standard PYTHIA simulation are shown as open circles and the events from the PYTHIA simulation containing 10% photon exchange processes are shown as stars. The errors are statistical only. A full detector simulation has been applied to the Monte Carlo event samples.

 

Figure:   The distribution of the fraction of events containing a gap, $f(\Delta\eta)$, with respect to $\Delta\eta$. The black dots represent the data, the open circles represent the standard hard photoproduction simulated events and the stars represent the simulated event sample of which 10% is due to photon exchange processes. The errors are statistical only, no correction for detector effects has been made, and the Monte Carlo samples have been passed through a detailed simulation of the ZEUS detector acceptance and smearing.

A comparison of the gap-fractions for data and Monte Carlo events in Figure 7 reveals an excess in the fraction of gap events in the data over that expected for standard hard photoproduction processes. Additionally, the data exhibit a two-component behaviour. There is an exponential fall at low values of $\Delta\eta$, but there is little or no dependence of $f(\Delta\eta)$ on $\Delta\eta$ for $\Delta\eta \gt 3.2$.We recall the definition of diffraction proposed in Sect. 1.2. One is tempted to interpret the exponential fall of $f(\Delta\eta)$ as being due to the production of gaps in non-diffractive processes. Then the flat component which dominates the rate of rapidity gap event production at large $\Delta\eta$ may be naturally interpreted as arising from a diffractive process. However we must check first that this two-component behaviour of $f(\Delta\eta)$ survives a full correction for detector acceptance and smearing. A detailed description of the correction method and the assignment of systematic errors may be obtained elsewhere [1,12].

The measured gap-fraction, corrected for detector effects, is shown in Figure 8 (black dots). The statistical errors are shown by the inner error bar and the systematic uncertainties combined in quadrature with the statistical errors are indicated by the outer error bars. (The data are the same in Figures 8(a) and (b).)

 

Figure:   Corrected gap-fraction. The data are shown as black dots. The inner error bar shows the statistical error and the outer error bar shows the systematic uncertainty combined in quadrature with the statistical error. The open circles in (a) show the expectation from PYTHIA for standard hard photoproduction processes. The solid line in (b) shows the result of a fit to an exponential plus a constant dependence where the dotted and dashed lines show the exponential and constant terms respectively.

Although there is some migration of events the overall detector corrections do not significantly affect the gap-fraction.

The corrected gap-fraction is compared with the prediction of the PYTHIA Monte Carlo program for standard hard photoproduction processes in Figure 8(a). (The PYTHIA prediction is shown by the open circles.) There is a significant discrepancy between the data and the prediction in the bin corresponding to $\Delta\eta \gt 3.5$. If we let the Monte Carlo prediction represent our expectation for the behaviour of the gap-fraction for non-diffractive processes then we can obtain an estimate of the diffractive contribution to the data by subtracting the Monte Carlo gap-fraction from the data gap-fraction. We obtain $.07 \pm .03$.Therefore we estimate that 7% of the data are due to hard diffractive processes.

In Figure 8(b) a second method of estimating the contribution from diffractive processes is illustrated. Here we have made direct use of the definition of diffraction quoted in Sect. 1.2. We have performed a two-parameter $\chi^2$ fit of the data to the sum of an exponential term and a constant term, constraining the sum to equal 1 at $\Delta\eta = 2$. (Below $\Delta\eta = 2$ the jet cones are overlapping in $\eta$.) The diffractive contribution which is the magnitude of the constant term is thus obtained from all four of the measured data points. It is $0.07 \pm 0.02(stat.) ^{+0.01} _{-0.02}(sys.)$ or again, 7% of the data are due to hard diffractive processes.

A caveat is in order. Implicit in both methods of estimating the fraction of diffractive processes in the data is the assumption that exactly 100% of hard diffractive scatterings will give rise to a rapidity gap. In fact this is considered to be an overestimate. Interactions between the $\gamma$ and p spectator particles can occur which would fill in the gap. Therefore the result of $0.07 \pm 0.02(stat.) ^{+0.01} _{-0.02}(sys.)$should be interpreted as a lower limit on the fraction of hard diffractive processes present in the data.

The probability of no secondary interaction occurring has been called the gap survival probability [13]. Estimates for the survival probability in pp interactions range between 5% and 30% [13,14,15]. However for these $\gamma p$ collisions we expect the survival probability to be higher due (in part) to the high values of $x_{\gamma}$ of this data sample compared to typical values of x_p in a pp data sample. Therefore we do not consider the ZEUS result to be incompatible with the D0 result, $0.0107 \pm 0.0010(stat.) ^{+0.0025}_{-0.0013}(sys.)$ [16], and the CDF result, $0.0086 \pm 0.0012$ [17].

In summary, ZEUS has measured the fraction of dijet events which contain a rapidity gap between the jets, $f(\Delta\eta)$. From a comparison of the uncorrected $f(\Delta\eta)$ with that obtained from the PYTHIA simulation of hard photoproduction processes (with full detector simulation) we conclude that the data are inconsistent with a completely non-diffractive production mechanism. From the behaviour of the fully corrected $f(\Delta\eta)$, we determine that the hard diffractive contribution to the dijet sample is greater than $(7 \pm 3)\%$. This value is obtained for two different methods of estimating the non-diffractive contribution, i) letting the non-diffractive contribution be represented by the PYTHIA prediction for hard photoproduction processes and ii) obtaining the non-diffractive contribution directly from an exponential fit to the data.