# Probing the gluon Sivers function in $p^\uparrow p\to J/\psi\,X$ and $p^\uparrow p \to D\,X$

## TL;DR

This paper investigates transverse single-spin asymmetries in proton-proton collisions producing J/psi and D mesons, aiming to extract information about the gluon Sivers function and distinguish between different theoretical models.

## Contribution

It introduces a method to separate two universal gluon Sivers functions using specific observables in polarized proton collisions, comparing GPM and CGI-GPM frameworks.

## Key findings

- Different processes are sensitive to different gluon Sivers functions.
- Proposed observables can enable separate extraction of two gluon Sivers functions.
- Comparison with experimental data can discriminate between GPM and CGI-GPM models.

## Abstract

We present a study of transverse single-spin asymmetries (SSAs) in $p^\uparrow p\to J/\psi\,X$ and $p^\uparrow p\to D X$ within the framework of the generalized parton model (GPM), which includes both spin and transverse momentum effects, and show how they can provide useful information on the still almost unknown gluon Sivers function. Moreover, by adopting a modified version of this model, named color gauge invariant (CGI) GPM, we analyze the impact of the initial- and final-state interactions on our predictions. As a consequence, we find that these two processes are sensitive to different gluon Sivers functions, which can be expressed as linear combinations of two distinct, universal gluon distributions. We therefore define proper observables which could allow for a separate extraction of these two independent Sivers functions. At the same time, we show how it would be possible to discriminate between the GPM and the CGI-GPM approaches by comparing the corresponding estimates of SSAs with present and future experimental results at RHIC.