A Parton Model for Diffractive Processes in Deep Inelastic Scattering

We demonstrate that the global properties of the “rapidity gap” events, observed at HERA, can be understood based on electron-gluon scattering as the underlying partonic process. Using the measured inclusive structure function F2 to determine the parameters of the parton model, the diffractive structure function F 2 is predicted. The ratio of diffractive and inclusive cross sections, RD = σD/σincl ≃ 1/9, is determined by the probability of the produced quark-antiquark pair to evolve into a colour singlet state. This colour singlet cluster may fragment into hadrons independently of the proton remnant, yielding the observed gap in rapidity. In the “rapidity gap” events, observed in deep inelastic scattering at HERA [1]-[3], the detected hadronic final state has small invariant mass, and it is separated by a gap in rapidity from the proton beam direction. The absence of a hadronic energy flow between proton remnant and current fragment suggests that in the scattering process a colour neutral part of the proton is stripped off which fragments independently of the proton. In analogy to hadronic processes of similar kind the “rapidity gap” events are also called “diffractive” events. The measured “diffractive” cross section is not suppressed at large values of the momentum transfer Q relative to the inclusive cross section. Such a “leading twist” behaviour is usually regarded as evidence for scattering on point-like constituents. This interpretation, however, appears to be in conflict with the fact that quarks and gluons, the constituents of the proton, carry colour. Hence, one expects the formation of jets in the final state with a hadronic energy flow familiar from ordinary deep inelastic scattering events without a rapidity gap. In the following we shall demonstrate that this puzzle can be resolved by taking nonperturbative fragmentation effects into account. We start from the production of a quarkantiquark pair in electron-gluon scattering as basic partonic process. Immediately after their production quark and antiquark propagate in the colour field of the proton. With a certain probability, approximated by a statistical weight factor, the quark-antiquark pair evolves into a colour singlet parton cluster which can escape from the proton and fragment independently into hadrons. The cross section for diffractive events can then be calculated in terms of the statistical weight factor, the quark-antiquark production cross section and the gluon density which we determine in terms of the inclusive structure function F2. Our approach is related to previous work on “aligned jet models” [4]-[6] and “wee parton lumps” in deep inelastic scattering [7, 8]. Quark-antiquark pairs are produced in electron-gluon scattering. The relevant kinematic variables are (cf. fig. 1) s = (P + k) , Q = −q = xys , x = Q 2P · q , (1) which characterize inclusive deep inelastic scattering, and the invariant mass M of the quark-antiquark pair, M = (q + pg) 2 . (2) With ~pg = ξ ~ P and −p 2 g = m 2 g ≪ Q ,M one has, β ≡ Q Q2 +M2 ≃ x ξ . (3)