Contribution of Twist-3 Multi-Gluon Correlation Functions to Single Spin Asymmetry in Semi-Inclusive Deep Inelastic Scattering

TL;DR

This paper investigates how twist-3 three-gluon correlation functions contribute to single spin asymmetries in semi-inclusive deep inelastic scattering, providing a new cross-section formula and clarifying discrepancies with previous results.

Contribution

It defines a complete set of three-gluon correlation functions and derives a new formula for their contribution to single-spin-dependent cross sections in SIDIS.

Findings

Derived a new cross-section formula for three-gluon contributions.

Clarified the discrepancy with previous literature.

Identified the complete set of relevant three-gluon correlation functions.

Abstract

As a possible source of the single transverse spin asymmetry, we study the contribution from purely gluonic correlation represented by the twist-3 ``three-gluon correlation" functions in the transversely polarized nucleon. We first define a complete set of the relevant three-gluon correlation functions, and then derive its contribution to the twist-3 single-spin-dependent cross section for the $D$-meson production in semi-inclusive deep inelastic scattering, which is relevant to determine the three-gluon correlations. Our cross-section formula differs from the corresponding result in the literature, and the origin of the discrepancy is clarified.