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

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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