Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements

In this letter, we show that it is necessary to include the full treatment of QCD evolution of Transverse Momentum Dependent parton densities to explain discrepancies between HERMES data and recent COMPASS data on a proton target for the Sivers transverse single spin asymmetry in Semi-Inclusive Deep Inelastic Scattering (SIDIS). Calculations based on existing fits to TMDs in SIDIS, and including evolution within the Collins-Soper-Sterman with properly defined TMD PDFs are shown to provide a good explanation for the discrepancy. The non-perturbative input needed for the implementation of evolution is taken from earlier analyses of unpolarized Drell-Yan (DY) scattering at high energy. Its success in describing the Sivers function in SIDIS data at much lower energies is strong evidence in support of the unifying aspect of the QCD TMD-factorization formalism