Novel Master Formula for Twist-3 Soft-Gluon-Pole Mechanism to Single Transverse-Spin Asymmetry

TL;DR

This paper demonstrates that the twist-3 soft-gluon-pole cross section for single transverse-spin asymmetries can be derived from a universal twist-2 cross section, revealing a fundamental structure and simplifying calculations for massless particle production.

Contribution

It introduces a master formula linking twist-3 SGP cross sections to twist-2 cross sections, highlighting a universal structure and the role of scale invariance in leading order perturbative QCD.

Findings

SGP cross section determined by a primordial twist-2 cross section

Universal structure behind SGP cross sections in various processes

Simplification of SGP cross sections for massless particle production

Abstract

We prove that twist-3 soft-gluon-pole (SGP) cross section for single spin asymmetries is determined by a certain ``primordial'' twist-2 cross section up to kinematic and color factors in the leading order perturbative QCD. This unveils universal structure behind the SGP cross sections in a variety of hard processes, and also the special role of the scale invariance in the corresponding primordial cross section, which leads to remarkable simplification of the SGP cross sections for the production of massless particle, such as those for pion production p^\uparrow p \to \pi X and direct-photon production p^\uparrow p \to \gamma X.