A Parametrisation of the Inclusive Diffractive Cross Section at HERA

A recently proposed parametrization for the deep inelastic diffractive cross section is used to describe the H1 94 data. We find two possible solutions, and we discuss them is some detail. 1. Diffractive events at HERA [1, 2] are generally attributed to the exchange of the Pomeron between the virtual photon and the proton. After the first observation of these events, attempts of a theoretical description [3] where based upon the idea of Ingelman and Schlein [4], and they viewed diffraction in deep inelastic scattering as “deep inelastic scattering on a Pomeron“. As a striking result along these lines, H1 [1] reported on a “hard gluon component of the Pomeron“ (where “hard“ refers to the behavior of the structure function near β = 1). However, with increasing statistics both ZEUS and H1 [1, 2] found evidence that in DIS diffraction the Pomeron intercept tends to be higher than the soft hadronic Pomeron. This observation suggested that the diffractive cross section at HERA contains both a soft and a hard component, and the latter one is stronger than initially expected. A theoretical description of the inclusive diffractive cross section, therefore, should contain both a nonperturbative Pomeron part and a perturbative contribution. As a possible strategy, one could start from that part of the final state where pQCD can be used safely, and then attempt to find a smooth extrapolation into the nonperturbative Regge region. As to the Pomeron, in the perturbative region it is most easily modelled by a two gluon-system, the gluon structure function of the proton. In the nonperturbative region, this model of a “hard Pomeron“ should smoothly connect with the soft hadronic Pomeron. Recently [5] a parametrization of the diffractive cross section has been proposed which follows this line of arguments, and it has been applied to both ZEUS and H1 data. For the latter the kinematic region was restricted to those values of β, Q, and xIP for which also ZEUS data points exist. As a striking result, it was found that the ZEUS data allow for a unique and rather succesful description whereas for the H1 data two different fits of this model were found. In the present paper we apply the parametrization of [5] to the complete H1 94 data of the diffractive cross section. We confirm the existence of two different solutions and we study their properties in some detail. Let us first briefly recapitulate the parametrization. It consists of 3 terms each of which stands for a particular diffractive final state: F D(3),I 2 = A ( x0 xIP )n2 β(1− β) (1) F D(3),II 2 = B ( x0 xIP )n2 αS (