Collinear Factorization for Single Transverse-Spin Asymmetry in Drell-Yan Processes

TL;DR

This paper derives the complete collinear factorization formula for single transverse-spin asymmetry in Drell-Yan processes, identifying various pole contributions and their perturbative origins, using a novel method.

Contribution

It introduces a new approach to derive the factorization of SSA, explicitly calculating all relevant perturbative coefficient functions at leading order.

Findings

Factorization formula includes hard-, soft-quark-, and soft-gluon-pole contributions.

Soft-quark- and soft-gluon-pole functions are obtained from one-loop amplitudes.

Hard-pole functions are derived from tree-level amplitudes.

Abstract

We study the scattering of a single parton state with a multi-parton state to derive the complete results of perturbative coefficient functions at leading order, which appear in the collinear factorization for Single transverse-Spin Asymmetry(SSA) in Drell-Yan processes with a transversely polarized hadron in the initial state. We find that the factorization formula of SSA contains hard-pole-, soft-quark-pole- and soft-gluon-pole contributions. It is interesting to note that the leading order perturbative coefficient functions of soft-quark-pole- and soft-gluon-pole contributions are extracted from parton scattering amplitudes at one-loop, while the functions of hard-pole contributions are extracted from the tree level amplitudes at tree-level. Our method to derive the factorization of SSA is different than the existing one in literature. A comparison of our results with those obtained by other method is made.