Single Transverse Spin Asymmetries at Parton Level

TL;DR

This paper investigates the validity of two factorization approaches for single transverse spin asymmetries at the parton level, revealing differences from hadron-level derivations and confirming previous massive parton results.

Contribution

It demonstrates that collinear factorization at the parton level differs from that at the hadron level, providing new insights into spin asymmetry factorization.

Findings

Collinear factorization at parton level differs from hadron level.

Constructed massless parton states to derive asymmetries.

Confirmed previous results with massive partons.

Abstract

Two factorization approaches have been proposed for single transverse spin asymmetries. One is the collinear factorization, another is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with parton states. We examine these two factorizations at parton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless partons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable parton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.