A simple nuclear-style mean field absorption/spin-orbit model for the Sivers function of the nucleon

I study the effect of scalar and spin-orbit absorption potentials, in the production of a nonzero Sivers-like asymmetry in hadron-hadron high energy collisions (Drell-Yan and single spin asymmetries). A basic model is built for the intrinsic state of a quark in the projectile hadron. S-wave and P-wave 2-component states are considered. Before the hard event, this quark is subject to absorbing scalar and spin-orbit local mean fields simulating interactions with a composite target. The relevant interaction terms are found to be the imaginary diagonal spin-orbit ones. Spin rotating terms, and scalar absorption, are not decisive. For $x$ $=$ 0 the found Sivers asymmetry vanishes, while at larger $x$ its qualitative dependence on $x$, $K_T$ follows the usual trends met in available models and parameterizations. Given the present-day knowledge of the considered phenomenological interactions, it is not possible to establish whether the related Sivers-like asymmetry is a leading twist one.