Introduction: maps of the pomeron

At the last Durham workshop on HERA physics, HERA was heralded as the new frontier for QCD. In the proceedings from that workshop, there was one theoretical contribution on ``Partons and QCD effects in the pomeron" [1]. Experimentally, the large rapidity gap events in deep inelastic scattering were yet to be discovered and the first preliminary results on photoproduced vector mesons were just starting to appear. Two years later, this workshop focuses on ``proton, photon and pomeron structure": the inclusion of the word ``pomeron" in the title of the workshop reflects a series of diffractive measurements which have been made in the intervening period at HERA. This talk is therefore an opportunity to discuss ``Measurements of partons and QCD effects in the pomeron", based on results from the H1 and ZEUS collaborations.

The diffractive processes studied are of the form:

where the the photon dissociates into the system X and the outgoing proton, p', remains intact, corresponding to single dissociation. The measurements are made as a function of the photon virtuality, the centre-of-mass energy of the virtual-photon proton system, , the mass of the dissociated system, X, denoted by M² and the four-momentum transfer at the proton vertex, given by .

The subject of diffraction is far from new: diffractive processes have been measured and studied for more than thirty years [2]. Their relation to the corresponding total cross sections at high energies has been successfully interpreted via the introduction of a single pomeron trajectory with a characteristic W² and t dependence [3]. The high-energy behaviour of the total cross sections is described by a power-law dependence on W²:

where W is measured in GeV, and is the pomeron intercept. The slow rise of hadron-hadron total cross sections with increasing energy indicates that the value of i.e. the total cross sections increase as W^0.16, although the latest data from CDF at  GeV indicate  [4]. The optical theorem relates the total cross sections to the elastic, and hence diffractive, scattering amplitude at the same W²:

where and GeV^-2 reflects the shrinkage of the diffractive peak with increasing W².

Whilst these Regge-based models give a unified description of all pre-HERA diffractive data, this approach is not fundamentally linked to the underlying theory of QCD. It has been anticipated that at HERA energies if either of the scales Q², M² or t become larger than the QCD scale , then it may be possible to apply perturbative QCD (pQCD) techniques, which predict changes to this power law behaviour, corresponding to an increase in the effective value of and a decrease of . This brings us from the regime of dominance of the slowly-rising ``soft" pomeron to the newly emergent ``hard" behaviour and the question of how a transition may occur between the two. Precisely where the Regge-based approach breaks down or where pQCD may be applicable is open to experimental question. The emphasis is therefore on the internal (in)consistency of a wide range of measurements of diffractive and total cross sections. As an experimentalist navigating around the various theoretical concepts of the pomeron, it is sometimes difficult to see which direction to take and what transitions occur where (Figure 1(a)). However, from an experimental perspective, the directions are clear, even if the map is far from complete (Figure 1(b)).

 
Figure 1: Maps of the pomeron: (a) theoretical and (b) experimental directions.

The HERA collider allows us to observe a broad range of diffractive phenomena at the highest values of W². What is new is that we have the ability to observe the variation of these cross sections at specific points on the M² scale, from the up to the system as discussed in section 2.1. Similarly, the production cross section can be explored as a function of Q², using a virtual photon probe. The high energy available provides a large rapidity span of 10 units ( ). The observation of a significant fraction of events ( ) with a large rapidity gap between the outgoing proton, p', and the rest of the final state, X, in deep inelastic scattering (DIS) has led to measurements of the internal structure of the pomeron. These results are discussed in section 2.2. Similar studies of events with high-p_T jets and a large rapidity gap have also been used to provide complementary information on this structure. Also, the observation of rapidity gaps between jets, corresponding to large t diffraction, are presented in section 2.3. Finally, a first analysis of the leading proton spectrometer data where the diffracted proton is directly measured is presented in section 2.4.