QCD evolution of the Sivers function

Abstract

We extend the Collins-Soper-Sterman (CSS) formalism to apply it to the spin-dependence governed by the Sivers function. We use it to give a correct numerical QCD evolution of existing fixedscale fits of the Sivers function. With the aid of approximations useful for the non-perturbative region, we present the results as parametrizations of a Gaussian form in transverse momentum space, rather than in the Fourier conjugate transverse coordinate space normally used in the CSS formalism. They are specifically valid at small transverse momentum. Since evolution has been applied, our results can be used to make predictions for Drell-Yan and semi-inclusive deep inelastic scattering at energies different from those where the original fits were made. Our evolved functions are of a form that they can be used in the same parton model factorization formulas as used in the original fits, but now with a predicted scale dependence in the fit parameters. We also present a method by which our evolved functions can be corrected to allow for twist-3 contributions at large parton transverse momentum.

I – Experimental investigation of transverse spin asymmetries in μ-p SIDIS processes: Collins asymmetries

“…This is a further evidence that, if there is a Q 2 dependence of the Collins asymmetry, it has to be weak, which suggests both transversity and Collins functions being leadingtwist quantities. Theoretical calculations of the Q 2 evolution of the transverse momentum dependent functions [29] are ongoing but not yet available for the Collins asymmetry.…”

Phenomenology of TMDs

“…Notice that the ratio in Eq. 24 is the same for the unpolarized TMD and the first derivative of the Sivers function [21]:…”

Lattice QCD calculations of transverse momentum-dependent parton distributions (TMDs)

“…additional to the wave function renormalizations of the quark operators; these divergences accordingly must ultimately be compensated by additional "soft factors", which are expected to be multiplicative and do not need to be specified in detail here, since only appropriate ratios in which they then presumably cancel will ultimately be considered. In order to regularize rapidity divergences, the staple direction v is taken slightly off the light cone into the space-like region [5,6], with perturbative evolution equations governing the approach to the light cone [7]. A useful parameter characterizing how close v is to the light cone is the Collins-Soper evolution parameterζ = v · P/(|v| |P|), in terms of which the light cone is approached forζ → ∞.…”

“…Corresponding signatures have emerged at COMPASS, HERMES and JLab [2][3][4], and that has motivated targeting a significant part of the physics program at future experiments in this direction, e.g., at the upgraded a e-mail: engel@nmsu.edu JLab 12 GeV facility and at the proposed electron-ion collider (EIC). Relating the experimental signature to the hadron structure encoded in TMDs requires a suitable factorization framework, the one having been advanced in [5][6][7][8] being particularly well-suited for connecting phenomenology to Lattice QCD. Factorization in the TMD context is considerably more involved than standard collinear factorization, with the resulting TMDs in general being process-dependent, via initial and/or final state interactions between the struck quark and the hadron remnant.…”