Novel effects in twist-three SSA

TL;DR

This paper investigates the role of gluon poles and gauge invariance in twist-three single spin asymmetries for Drell-Yan and direct photon production, revealing new diagrams and twist-3 contributions.

Contribution

It demonstrates the necessity of new diagrams for gauge invariance and identifies additional twist-3 terms in direct photon production, advancing understanding of SSA mechanisms.

Findings

Gluon poles are absent in certain correlators in Feynman gauge.

New non-standard diagrams are required for gauge invariance.

Additional twist-3 terms are found in direct photon production.

Abstract

We discuss the role of gluon poles and the gauge invariance for the hadron tensors of Drell-Yan and direct photon production processes with the transversely polarized hadron. These hadron tensors are needed to construct the corresponding single spin asymmetries. For the Drell-Yan process, we perform our analysis within both the Feynman and axial-type (contour) gauges for gluons. In both the Feynman and contour gauges, we demonstrate that the gauge invariance leads to the need of the new (non-standard) diagrams. Moreover, in the Feynman gauge, we argue the absence of gluon poles in the correlators $\langle\bar\psi\gamma_\perp A^+\psi\rangle$ related traditionally to $dT(x,x)/dx$. As a result, these terms disappear from the final QED gauge invariant Drell-Yan hadron tensor. For the direct photon production, by using the contour gauge for gluon fields, we find that there are new twist-$3$ terms present in the hadron tensor of the considering process in addition to the standard twist-$3$ terms.