# Computing the gluon Sivers function at small-$x$

## TL;DR

This paper calculates the gluon Sivers function at small-x using the Odderon, revealing non-factorization effects and potential sign changes in spin asymmetries, with implications for future collider experiments.

## Contribution

It introduces a novel method to compute the gluon Sivers function at small-x by linking it to the Odderon and solves the evolution equations numerically.

## Key findings

- x and k_perp dependences do not factorize due to quantum evolution
- Factorization breaking is mild compared to unpolarized TMDs
- Single spin asymmetry in open charm production may flip sign, testable at EIC

## Abstract

We compute the gluon Sivers function $f_{1T}^{\perp g}(x,k_\perp)$ of the transversely polarized nucleon at small-$x$ by exploiting the known connection between the dipole gluon Sivers function and the Odderon. We numerically solve the evolution equation for the Odderon both in the linear and nonlinear regimes. While we find that the $x$ and $k_\perp$ dependences of the Sivers function do not factorize as a result of the quantum evolution, factorization breaking is not numerically significant, and is much milder than what one expects in the case of unpolarized TMDs. We also point out the possibility that, due to the presence of a node in the Sivers function, single spin asymmetry for open charm production in semi-inclusive deep inelastic scattering flips signs as the transverse momentum of D-mesons is varied. This can be tested at the future Electron-Ion Collider.