The gluon Sivers distribution: status and future prospects

TL;DR

This review summarizes current knowledge and future prospects for understanding the gluon Sivers distribution, highlighting experimental challenges, theoretical considerations, and promising processes for direct measurement in various high-energy collision experiments.

Contribution

It provides a comprehensive overview of the status of gluon Sivers function research and discusses future experimental opportunities and theoretical constraints.

Findings

Current data do not tightly constrain the gluon Sivers function.

SIDIS data allows for a gluon Sivers contribution consistent with large N_c expectations.

Multiple promising processes for direct measurement are identified, emphasizing the importance of diverse experimental approaches.

Abstract

This is a review of what is currently known about the gluon Sivers distribution and of what are the opportunities to learn more about it. Because single transverse spin asymmetries in $p^\uparrow \, p \to \pi \, X$ provide only indirect information about the gluon Sivers function through the relation with the quark-gluon and tri-gluon Qiu-Sterman functions, current data from hadronic collisions at RHIC have not yet been translated into a solid constraint on the gluon Sivers function. SIDIS data, including the COMPASS deuteron data, allow for a gluon Sivers contribution that is of the natural size expected from large $N_c$ arguments, which is ${\cal O}(1/N_c)$ times the nonsinglet quark Sivers contribution. Several very promising processes to measure the gluon Sivers effect directly have been put forward, which apart from ongoing and future investigations at RHIC, would strongly favor experiments at AFTER@LHC and a possible future Electron-Ion Collider. Due to the inherent process dependence of TMDs, the gluon Sivers TMD probed in the various processes are not necessarily the same, but rather can be different linear combinations of two universal gluon Sivers functions that have different behavior under charge conjugation and that therefore satisfy different theoretical constraints. For this reason both hadronic and DIS type of collisions are essential in the study of the role of gluons in transversely polarized protons.