A quark model analysis of the Sivers function

TL;DR

The paper develops a general, NR-reduced formalism to compute the Sivers function within Constituent Quark Models and applies it to the Isgur-Karl framework. It finds sizable valence-quark Sivers effects with opposite signs for u and d, aligning with insights from impact-parameter dependent GPDs and satisfying the Burkardt sum rule at the hadronic scale. By performing a crude QCD evolution of the Sivers moments to the experimental scale, the authors show improved agreement with SIDIS data, suggesting the CQM approach can capture essential features of the Sivers function. The work also highlights the link between Sivers TMDs and IPD GPDs and provides a practical path for evaluating other CQMs within this formalism.

Abstract

We develop a formalism to evaluate the Sivers function. The approach is well suited for calculations which use constituent quark models to describe the structure of the nucleon. A non-relativistic reduction of the scheme is performed and applied to the Isgur-Karl model of hadron structure. The results obtained are consistent with a sizable Sivers effect and the signs for the u and d flavor contributions turn out to be opposite. This pattern is in agreement with the one found analyzing, in the same model, the impact parameter dependent generalized parton distributions. The Burkardt Sum Rule turns out to be fulfilled to a large extent. We estimate the QCD evolution of our results from the momentum scale of the model to the experimental one and obtain reasonable agreement with the available data.