Extraction of the Sivers Function from SIDIS, Drell-Yan, and W^{±}/Z Data at Next-to-Next-to-Next-to Leading Order.

We perform the global analysis of polarized semi-inclusive deep inelastic scattering (SIDIS), pion-induced polarized Drell-Yan (DY) process, and W^{±}/Z boson production data and extract the Sivers function for u, d, s and for sea quarks. We use the framework of transverse momentum dependent factorization at next-to-next-to-next-to leading order (N^{3}LO) accuracy. The Qiu-Sterman function is determined in a model independent way from the extracted Sivers function.

Self-Contained Definition of the Collins-Soper Kernel.

The rapidity anomalous dimension (RAD), or Collins-Soper kernel, defines the scaling properties of transverse momentum dependent distributions and can be extracted from the experimental data. I derive a self-contained nonperturbative definition that represents RAD without reference to a particular process. This definition makes possible exploration of the properties of RAD by theoretical methods on one side, and the properties of QCD vacuum with collider measurements on another side.

Correspondence between Soft and Rapidity Anomalous Dimensions.

We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal mapping between scattering geometries. The correspondence is valid to all orders of perturbation theory and in this way, provides one with a proof of rapidity renormalization procedure for multiparton scattering [including the transverse momentum dependent (TMD) factorization as a special case].