Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: the role of the three-gluon correlator

TL;DR

This paper investigates the Sivers asymmetry in semi-inclusive deep inelastic scattering, focusing on the role of three-gluon correlators at next-to-leading order, bridging collinear and TMD factorization formalisms.

Contribution

It introduces a detailed NLO calculation of the transverse momentum-weighted Sivers asymmetry involving three-gluon correlators and connects collinear twist-3 and TMD frameworks.

Findings

Derived coefficient functions for TMD evolution related to three-gluon correlators.

Performed NLO calculation of spin-dependent cross section involving three-gluon functions.

Identified off-diagonal contributions to the evolution of the Qiu-Sterman function.

Abstract

We study the Sivers asymmetry in semi-inclusive hadron production in deep inelastic scattering. We concentrate on the contribution from the photon-gluon fusion channel at ${\cal O}(\alpha_{em}^2 \alpha_s)$, where three-gluon correlation functions play a major role within the twist-3 collinear factorization formalism. We establish the correspondence between such a formalism with three gluon correlation functions and the usual transverse momentum dependent (TMD) factorization formalism at moderate hadron transverse momenta. We derive the coefficient functions used in the usual TMD evolution formalism related to the quark Sivers function expansion in terms of the three-gluon correlation functions. We further perform the next-to-leading order calculation for the transverse-momentum-weighted spin-dependent differential cross section, and identify the off-diagonal contribution from the three-gluon correlation functions to the QCD collinear evolution of the twist-3 Qiu-Sterman function.