Transverse Single Spin Asymmetry in $p+p^\uparrow \to D +X $

TL;DR

This paper predicts the single spin asymmetry in D-meson production at RHIC energies using a generalized parton model and recent gluon Sivers function fits, analyzing the effects of TMD evolution on the asymmetry.

Contribution

It provides new predictions for D-meson SSA at various energies and investigates the impact of TMD evolution on these asymmetries.

Findings

Predicted asymmetries range from 0.5% to 10% at RHIC energies.

TMD evolution reduces asymmetry predictions by a factor of 3 or more.

Predictions vary across different experimental energies and conditions.

Abstract

We present expected values of the Single Spin Asymmetry (SSA) in $D$-meson production in the process $p+p^\uparrow \rightarrow D^0 + X $ at RHIC energy $(\sqrt{s}=200\text{ GeV})$ using a generalized parton model approach. We use fits to the gluon Sivers function obtained recently by D'Alesio {\it et al.,} by fitting to the asymmetry data for the process $p+p^\uparrow \rightarrow \pi^0+ X$ measured by the PHENIX collaboration at RHIC. These fits give peak asymmetry predictions which lie in a broad range, $0.5\%\lesssim A_N\lesssim10\%$ for the kinematic regions considered. This is to be compared with the upper bound of 18\% expected for the maximal gluon Sivers function. We extend our analysis to two other centre of mass energies of proposed experiments - AFTER@LHC $(\sqrt{s}=115\text{ GeV})$ and a future RHIC run $(\sqrt{s}=500\text{ GeV})$. We further investigate (at $\sqrt{s}=200$ GeV) the effect of the transverse momentum dependent (TMD) evolution of the unpolarized parton distribution functions (pdf's) and of the gluon Sivers function on the asymmetry predictions. We perform this study using an evolution setup given by Anselmino {\it et al}. We find that the effect of evolution is an overall reduction of the asymmetry predictions. For example, for the saturated gluon Sivers function, upon taking into account TMD evolution, peak asymmetry predictions reduce by a factor 3 or more. This decrease is similar to that noticed earlier for Single Spin Asymmetries (SSA) in the electroproduction of $J/\psi$.