Inclusive and Diffractive Structure Functions at Small x
W. Buchmuller, T. Gehrmann, A. Hebecker
TL;DR
This work develops a unified semiclassical framework for inclusive and diffractive DIS at small $x$, expressing quark and gluon distributions through Wilson-loop correlators that encode the proton's soft colour field. Initial non-perturbative inputs at a low scale $Q_0^2$ are generated by a simple averaging model with a few parameters, and standard LO DGLAP evolution then describes the $Q^2$-dependence, with the gluon distribution driving the rise of structure functions. The authors demonstrate that both $F_2(x,Q^2)$ and $F_2^{D(3)}(\xi,\beta,Q^2)$ can be described with a small set of parameters, and they show that the energy dependence arises from non-perturbative soft-field averaging, common to inclusive and diffractive channels. The framework yields concrete predictions for diffractive parton distributions, charm content, and the $\beta$-dependence of diffraction, enabling tests of the color-field averaging model and potential extensions to alternative averaging schemes.
Abstract
In the semiclassical approach, inclusive and diffractive quark and gluon distributions are expressed in terms of correlation functions of Wilson loops. Each Wilson loop integrates the colour field strength in the area between the trajectories of two fast partons penetrating the proton. We introduce a specific model for averaging over the relevant colour field configurations. Within this model, all parton distributions at some low scale Q_0^2 are given in terms of three parameters. Inclusive and diffractive structure functions at higher values of Q^2 are determined in a leading-order QCD analysis. In both cases, the evolution is driven by a large gluon distribution. A satisfactory description of the structure functions F_2(x,Q^2) and F_2^D(3)(xi,beta,Q^2) is obtained. The observed rise of F_2^D(3) with xi is parametrized by a non-perturbative logarithmic energy dependence, compatible with unitarity. In our analysis, the observed rise of F_2 at small x is largely due to the same effect.