Phenomenology of Sivers Effect with TMD Evolution

Abstract

Following the TMD evolution scheme recently proposed for the unpolarized and the Sivers distribution function, we propose a simple strategy to take into account this TMD Q 2 dependence in our phenomenological extraction of the Sivers function from SIDIS data. New results are presented and possible future applications are discussed. The exploration of the 3-dimensional structure of the nucleon, both in momentum and in conguration space, is one of the major issues in high energy hadron physics. Information on this 3-dimensional structure is embedded in the Transverse Momentum Dependent distribution and fragmentation functions (TMDs). The Sivers function, which describes the number density of unpolarized quarks inside a transversely polarized proton, is particularly interesting, as it might provide information on the partonic orbital angular momentum. So far, all phenomenological ts have either neglected the QCD scale dependence of TMDs (which was unknown) or limited it to the collinear part of the unpolarized PDFs, according to the DGLAP evolution. Here, we present the rst attempt to take into account the TMD evolution as proposed by Aybat, Collins, Qiu and Rogers [1, 2, 3] in the analysis of the Sivers asymmetry data and show how these new results compare with the previous extractions. Eventually, such a scheme will provide a complete TMD factorization framework for a consistent treatment of all SIDIS data. In Ref. [4] we showed how the QCD evolution equation of the TMDs in the coordinate space proposed in Refs. [2] and [3] can be expressed in a simplied way, taking the renormalization scale 2 and the regulating parameters F and D all equal to Q 2 , as e