Scaling and Diffraction in Deep Inelastic Scattering

We pursue the hypothesis that the events with a large rapidity gap, observed at HERA, reflect the scattering of electrons off lumps of wee partons inside the proton. A simple scaling behaviour is predicted for the diffractive structure functions, which are related to the inclusive structure function F2(x,Q ) at small values of the scaling variable x. The results are compared with recent measurements of the diffractive structure function F 2 (x,Q ,M). In the so-called “rapidity gap” events, observed and studied at HERA [1]-[3], a system of hadrons is observed with small invariant mass and with a gap in rapidity in the hadronic energy flow adjacent to the proton beam direction. This suggests, that in the scattering process a colour neutral part of the proton with small momentum fraction is stripped off, which then fragments into the hadrons visible in the detector. The proton remnant, carrying most of the energy, escapes undetected close to the proton direction. The rapidity gap reflects the absense of a colour flow between proton and current fragments. In analogy to hadronic processes of similar kind the “rapidity gap” events are also referred to as “diffractive” events. It is a remarkable feature of this new class of events, that the cross section at large momentum transfer Q is not suppressed relative to the total inclusive cross section. Naively, one might expect that the rate for extracting more than one parton from the proton should rapidly decrease with increasing Q. This, however, is not the case. It is a theoretical challenge to derive the observed “leading twist” behaviour of the diffractive cross section from QCD, the theory of strong interactions. In a recent paper [4], we have proposed to describe the multi-parton processes underlying the diffractive events by means of an effective lagrangian which specifies the coupling between the virtual photon, the colour singlet wee parton cluster inside the proton and the hadronic final state. Together with further information on the cluster density and the mass spectrum of the final states, one then obtains a prediction for the diffractive differential cross section. Recently, the H1 collaboration at HERA has published a first measurement of the diffractive structure function F 2 for a large range of the kinematic variables [3]. In this letter, we therefore extend our previous work [4] and compare the results with the recent measurements as well as predictions of other theoretical approaches. We consider the inelastic scattering process e(k) + p(P ) → e(k) + p̃(P ) +X(PX) , (1) where p̃ andX denote the proton remnant and the detected hadronic system, respectively. From the four momenta k, P , P ′ = (1− ξ)P , q = k − k and PX = q + ξP one obtains the Lorentz invariant kinematic variables s = (k + P ) , Q = −q , x = Q 2q · P , M = (q + ξP ) . (2) In addition to the first three variables, which characterize ordinary deep inelastic scattering, the invariant mass M of the detected hadronic final state occurs as fourth variable.