The QCD Evolution of the Sivers Function

TL;DR

This paper extends the CSS formalism to include QCD evolution of the Sivers function, enabling accurate predictions for spin-dependent processes at various energies by providing evolved parametrizations in transverse momentum space.

Contribution

It introduces a method to evolve the Sivers function using QCD, with parametrizations suitable for small transverse momentum, and incorporates corrections for twist-3 contributions at high transverse momentum.

Findings

Provides evolved Sivers functions for different energy scales.

Offers parametrizations in Gaussian form for practical use.

Includes a method to account for twist-3 effects at large transverse momentum.

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 fixed-scale 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.