Factorization and Gauge Invariance of Twist-3 Cross Section for Single Spin Asymmetry

TL;DR

This paper establishes the factorization and gauge invariance of the twist-3 single-spin-dependent cross section in perturbative QCD, providing a complete formalism for SIDIS processes involving transversely polarized nucleons.

Contribution

It proves the factorization and gauge invariance of the twist-3 cross section, clarifying the role of Ward identities and deriving the complete cross section for SIDIS.

Findings

Confirmed the gauge invariance of the twist-3 cross section

Derived the full cross section for SIDIS with transversely polarized nucleons

Showed the absence of derivative terms due to consistency relations

Abstract

We prove factorization and gauge invariance of the twist-3 single-spin-dependent cross section in the leading order perturbative QCD, which was missing in the previous literature. We emphasize that the consistency relation from the Ward identities for color gauge invariance is crucial to guarantee the cancelation among the various gauge-noninvariant contributions in the cross section. This relation also proves the absence of the "derivative" terms in the cross section corresponding to the hard-pole and soft-fermion-pole contributions. Applying the formalism to SIDIS, $ep^\uparrow\to e\pi X$, we have derived the complete cross section associated with the twist-3 distribution for the transversely polarized nucleon.