Probing the gluon Sivers function through direct photon production at RHIC

We study the production of prompt photons at the RHIC in the context of a generalized parton model framework, with a view to obtain information on the gluon Sivers function (GSF). At RHIC energy (root s = 200 GeV), the Compton process gq -> gamma q contributes significantly to the production of direct photons at midrapidity and dominates it in the negative (backward) rapidity region. We find that for direct photons, asymmetries of up to 10% are allowed by a maximal gluon Sivers function. However, the asymmetry obtained using existing fits of the GSF available in the literature is negligible. We also estimate the impact that photons produced via fragmentation can have on the signal and find that their inclusion can dilute the asymmetry by between 10% and 50% of the direct photon value. Finally, using the color-gauge invariant generalized parton model (CGI-GPM) approach, we consider the effects of initial-state and final-state interactions which can affect the universality of the Sivers functions in different processes. We find that the inclusion of these effects leads to the size of the gluon contributions being roughly halved. However, in the backward region which we are interested in, the sizes of the quark contributions are suppressed even further, leading to increased dominance of the gluon contributions.