Solution of the off-forward leading logarithmic evolution equation based on the Gegenbauer moments inversion

TL;DR

This paper presents a method to solve the off-forward leading logarithmic evolution equation by leveraging conformal invariance and Gegenbauer moments, simplifying the problem to the well-understood DGLAP evolution.

Contribution

It introduces a novel approach that reduces off-forward evolution to forward evolution using Gegenbauer moments and provides explicit integral kernels for arbitrary skewness.

Findings

Derivation of integral kernels relating forward and off-forward functions.

Reduction of off-forward evolution to DGLAP evolution.

Explicit formulas valid for any skewness parameter.

Abstract

Using the conformal invariance the leading-log evolution of the off-forward structure function is reduced to the forward evolution described by the conventional DGLAP equation. The method relies on the fact that the anomalous dimensions of the Gegenbauer moments of the off-forward distribution are independent on the asymmetry, or skewedness, parameter and equal to the DGLAP ones. The integral kernels relating the forward and off-forward functions with the same Mellin and Gegenbauer moments are presented for arbitrary asymmetry value.