Odderon mechanism for transverse single spin asymmetry in the Wandzura-Wilczek approximation

Abstract

We compute the transverse single spin asymmetry in forward ${p}^{\ensuremath{\uparrow}}p\ensuremath{\rightarrow}hX$ and ${p}^{\ensuremath{\uparrow}}A\ensuremath{\rightarrow}hX$ collisions from the odderon mechanism originally suggested by Kovchegov and Sievert [Phys. Rev. D 86, 034028 (2012)]. Working in the hybrid approach of the color glass condensate effective theory, we first identify the relevant collinear parton distribution function (PDF) of the transversely polarized proton ${p}^{\ensuremath{\uparrow}}$ as the intrinsic twist-3 ${g}_{T}(x)$ distribution. We further argue that the complete polarized cross section also contains contributions from the kinematical and the dynamical twist-3 PDFs, in addition to the intrinsic twist-3 PDF. By restricting to the Wandzura-Wilczek approximation, where the dynamical twist-3 PDFs are dropped, we find that the odderon contribution to the polarized cross section for inclusive hadron production is exactly zero at the next-to-leading order in the strong coupling.