Soft-Gluon-Pole Contribution in Single Transverse-Spin Asymmetries of Drell-Yan Processes

TL;DR

This paper investigates the role of soft-gluon-pole contributions in the collinear factorization of single transverse-spin asymmetries in Drell-Yan processes, highlighting their necessity and consistency with previous results.

Contribution

It demonstrates the essential existence of soft-gluon-pole contributions in the factorization, derived from one-loop cross-sections, and clarifies their relation to hard-pole contributions and twist-3 operator evolution.

Findings

Soft-gluon-pole contributions are necessary for correct factorization.

Hard-pole contributions include an additional parton process.

The method can be extended to other processes and higher orders.

Abstract

We use multi-parton states to examine the leading order collinear factorization of single transverse-spin asymmetries in Drell-Yan processes. Twist-3 operators are involved in the factorization. We find that the so-called soft-gluon-pole contribution in the factorization must exist in order to make the factorization correct. This contribution comes from the corresponding cross-section at one-loop, while the hard-pole contribution in the factorization comes from the cross-section at tree-level. Although the two contributions come from results at different orders, their perturbative coefficient functions in the factorization are at the same order. This is in contrast to factorizations only involving twist-2 operators. The soft-gluon-pole contribution found in this work is in agreement with that derived in a different way. For the hard-pole contributions we find an extra contribution from an extra parton process contributing to the asymmetries. We also solve a part of discrepancy in evolutions of the twist-3 operator. The method presented here for analyzing the factorization can be generalized to other processes and can be easily used for studying factorizations at higher orders, because the involved calculations are of standard scattering amplitudes.