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

Understand

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.