Single spin asymmetry in forward $pA$ collisions from Pomeron-Odderon interference

Working in the hybrid framework of the high energy $pA$ collisions we identify a new contribution to transverse single spin asymmetry (SSA). The phase necessary for the SSA is provided by the Pomeron-Odderon interference in the dense nuclear target. The complete formula for the $pA\to hX$ polarized cross section also contains the transversity distribution for the polarized projectile as well as the real part of the twist-3 fragmentation function. We numerically estimate the asymmetry $A_N$ and its nuclear dependence. Based on a model computation we find that $A_N$ can be a percent level in the forward and low-$P_{h\perp }$ region. For large nuclei we find significant suppression, with $A_N\propto A^{-7\mathrm{/}6}$ parametrically. As a notable feature we find a node of $A_N$ as a function of the $P_{h\perp }$ around the values of the initial saturation scale that could be used to test this mechanism experimentally.