Quark Sivers Function at Small-$x$: Leading contribution from the Spin-Dependent Odderon

Abstract

We present the calculation of the leading contribution to the quark Sivers function at small-Bjorken $x$. This calculation uses the high energy scattering approximation and operator formalism developed by Kovchegov and Sievert to obtain a dominant contribution to the quark Sivers function coming from the spin-dependent odderon, in agreement with the results of Dong, Zhen, and Zhou. We then calculate this dominant contribution in the diquark model of the proton to obtain a small-$x$ estimate for the Sivers function.