Gauge Invariance and QCD Twist-3 Factorization for Single Spin Asymmetries

TL;DR

This paper investigates twist-3 collinear factorization in Drell-Yan processes, ensuring gauge invariance and clarifying the calculation of single spin asymmetries, with implications for higher order corrections and comparisons to semi-inclusive DIS.

Contribution

It demonstrates how gauge invariance is realized in twist-3 factorization and shows that virtual corrections are determined by the quark form factor, simplifying higher order calculations.

Findings

Agreement with previous results on single spin asymmetry

Construction of additional observables for spin effects

Virtual corrections linked to quark form factor

Abstract

The collinear factorization at twist-3 for Drell-Yan processes is studied with the motivation to solve the discrepancy in literature about the single spin asymmetry in the lepton angular distribution, and to show how QCD gauge invariance is realized in the hadronic tensor. The obtained result here agrees with our early result derived with a totally different approach. In addition to the asymmetry we can construct another two observables to identify the spin effect. We show that the gauge invariance of different contributions in the hadronic tensor is made in different ways by summing the effects of gluon exchanges. More interestingly is that we can show that the virtual correction to one structure function of the hadronic tensor, hence to some weighted SSA observables, is completely determined by the quark form factor. This will simplify the calculation of higher order corrections. The corresponding result in semi-inclusive DIS is also given for the comparison with Drell-Yan processes.