Partonic State and Single Transverse Spin Asymmetry in Drell-Yan Process

TL;DR

This paper investigates the theoretical foundations of single transverse-spin asymmetries in Drell-Yan processes by analyzing partonic states, confirming some aspects of TMD factorization while challenging the collinear approach.

Contribution

It provides a parton-level analysis of two factorization approaches for spin asymmetries, verifying TMD factorization results and questioning collinear factorization relations.

Findings

Reproduces TMD factorization results at parton level.

Partially verifies collinear factorization results.

Finds negative results for relations between Sivers function and twist-3 matrix element.

Abstract

Single transverse-spin asymmetries have been studied intensively both in experiment and theory. Theoretically, two factorization approaches have been proposed. One is by using transverse-momentum-dependent factorization and the asymmetry comes from the so called Sivers function. Another is by using collinear factorization where the nonperturbative effect is parameterized by a twist-3 hadronic matrix element. However, the factorized formulas for the asymmetries in the two approaches are derived at hadron level formally by diagram expansion, where one works with various parton density matrices of hadrons. If the two factorizations hold, they should also hold at parton level. We examine this for Drell-Yan processes by replacing hadrons with partons. By calculating the asymmetry, Sivers function and the twist-3 matrix element at nontrivial leading order of $\alpha_s$, we find that we can reproduce the result of the transverse-momentum-dependent factorization. But we can only verify the result of the collinear factorization partly. Two formally derived relations between Sivers function and the twist-3 matrix element are also examined with negative results.