We present expected values of the single spin asymmetry in $D$-meson production in the process $p+p^{\uparrow }\to D^0+X$ at RHIC energy $(\sqrt{s}=200\mathrm{GeV})$ using a generalized parton model approach. For this purpose, we use the fits to the gluon Sivers function recently obtained by D’Alesio, Murgia, and Pisano. We find that the peak asymmetry predictions for these lie in a broad range, $0.5\%\lesssim A_N\lesssim 10\%$, 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 center-of-mass energies of proposed experiments: AFTER@LHC $(\sqrt{s}=115\mathrm{GeV})$ and a future RHIC run $(\sqrt{s}=500\mathrm{GeV})$. We further investigate (at $\sqrt{s}=200\mathrm{GeV}$) the effect of the transverse-momentum-dependent evolution of the unpolarized parton distribution functions and of the gluon Sivers function on the asymmetry predictions. We find that the inclusion of evolution causes an overall reduction of the asymmetry predictions. For example, predictions for the peak asymmetry decrease by a factor of 3 or more for the case of the saturated gluon Sivers function. This decrease is similar to that noticed earlier for single spin asymmetry in the electroproduction of $J/\psi$.

• Received 8 August 2016

DOI:https://doi.org/10.1103/PhysRevD.94.114022