Master Formula for the Three-Gluon Contribution to Single Spin Asymmetry in Semi-Inclusive Deep Inelastic Scattering

TL;DR

This paper derives a comprehensive formula linking three-gluon correlations to single-spin asymmetries in semi-inclusive deep-inelastic scattering, simplifying calculations and revealing new structural insights.

Contribution

It introduces a master formula that connects three-gluon correlation functions to twist-3 single-spin asymmetries, extending previous quark-gluon based formulas.

Findings

The master formula simplifies the calculation of single-spin asymmetries involving three gluons.

It reduces complex subprocesses to Born cross sections for b3^*gd7 ce4c scattering.

Discussion of potential higher-order corrections extension.

Abstract

We derive a "master formula" for the contribution of the three-gluon correlation function in the nucleon to the twist-3 single-spin-dependent cross section for semi-inclusive deep-inelastic scattering, ep^\uparrow\to eDX. This is an extension of the similar formula known for the so-called soft-gluon-pole contribution induced by the quark-gluon correlation function in a variety of processes. Our master formula reduces the relevant interfering partonic subprocess with the participation of the three gluons to the Born cross sections for the \gamma^*g\to c\bar{c} scattering, which reveals the new structure behind the twist-3 single spin asymmetry and simplifies the actual calculation greatly. A possible extension to higher order corrections is also discussed.