A study on three gluon correlator of Sivers asymmetry in SIDIS

We study the three-gluon correlation function contribution to the Sivers asymmetry in semiinclusive deep inelastic scattering. We first establish the matching between the usual twist-3 collinear factorization approach and transverse momentum dependent factorization formalism for the moderate transverse momentum region. We then derive the so-called coefficient functions used in the usual TMD evolution formalism. Finally we perform the next-to-leading order calculation for the transverse-momentum-weighted spin-dependent differential cross section, from which we identify the QCD collinear evolution of the twist-3 Qiu-Sterman function: the offdiagonal contribution from the three-gluon correlation functions.