Evolution and models for skewed parton distributions

TL;DR

This paper explores the structure of skewed parton distributions using factorized models for double distributions, revealing how their profiles relate to usual parton distributions and analyzing their evolution patterns.

Contribution

It introduces a model linking double distributions to skewed parton distributions through profile functions and demonstrates their equivalence to recent models for small skewedness.

Findings

FW parts of SPDs can be derived from forward densities via averaging.

Asymptotic profiles determine the small-x behavior of double distributions.

Numerical evolution studies provide insights into SPD behavior over scales.

Abstract

We discuss the structure of the ``forward visible'' (FW) parts of double and skewed distributions related to usual distributions through reduction relations. We use factorized models for double distributions (DDs) f(x, alpha) in which one factor coincides with the usual (forward) parton distribution and another specifies the profile characterizing the spread of the longitudinal momentum transfer. The model DDs are used to construct skewed parton distributions (SPDs). For small skewedness, the FW parts of SPDs H(x, xi) can be obtained by averaging forward parton densities f(x- xi alpha) with the weight rho (alpha) coinciding with the profile function of the double distribution f(x, alpha) at small x. We show that if the x^n moments f_n (alpha) of DDs have the asymptotic (1-alpha^2)^{n+1} profile, then the alpha-profile of f (x,alpha) for small x is completely determined by small-x behavior of the usual parton distribution. We demonstrate that, for small xi, the model with asymptotic profiles for f_n (alpha) is equivalent to that proposed recently by Shuvaev et al., in which the Gegenbauer moments of SPDs do not depend on xi. We perform a numerical investigation of the evolution patterns of SPDs and gave interpretation of the results of these studies within the formalism of double distributions.