Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism
Abstract
We extend the improved Collins-Soper-Sterman (iCSS) W+Y construction recently presented in~Collins:2016hqq to the case of polarized observables, where we focus in particular on the Sivers effect in semi-inclusive deep-inelastic scattering. We further show how one recovers the expected leading-order collinear twist-3 result from a (weighted) qT-integral of the differential cross section. We are also able to demonstrate the validity of the well-known relation between the (TMD) Sivers function and the (collinear twist-3) Qiu-Sterman function within the iCSS framework. This relation allows for their interpretation as functions yielding the average transverse momentum of unpolarized quarks in a transversely polarized spin-12 target. We further outline how this study can be generalized to other polarized quantities.
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