Skewed and double distributions in pion and nucleon

TL;DR

This paper investigates the structure of skewed and double distributions in pions and nucleons, emphasizing the importance of including all twist-2 components, and computes these distributions in the pion using an effective chiral theory.

Contribution

It introduces a comprehensive representation of skewed distributions with a two-component structure and relates skewed distributions to distribution amplitudes via crossing relations.

Findings

Derived the two-component structure of skewed distributions.

Computed quark distributions in the pion at a low normalization point.

Established crossing relations linking skewed distributions to distribution amplitudes.

Abstract

We study the non-forward matrix elements of twist-2 QCD light-ray operators and their representations in terms of skewed and double distributions, considering the pion as well as the nucleon. We point out the importance of explicitly including all twist-2 structures in the double distribution representation, which naturally leads to a ``two-component'' structure of the skewed distribution, with different contributions in the regions |X| > xi/2 and |X| < \xi/2. We compute the skewed and double quark distributions in the pion at a low normalization point in the effective chiral theory based on the instanton vacuum. Also, we derive the crossing relations expressing the skewed quark distribution in the pion through the distribution amplitude for two--pion production. Measurement of the latter in two-pion production in gamma^* gamma and gamma^* N reactions could provide direct information about the skewed as well as the usual quark/antiquark-distribution in the pion.