Aspects of $χ$ and $ψ$ Production in Polarized Proton-Proton Collisions
Several topics of relevance to low transverse momentum $ψ$ and $χ_{1,2}(c\overline{c})$ production in polarized proton-proton collisions are discussed. The leading ${\cal O}(α_S^3)$ contributions to the low $p_T$ $χ_1$ production cross-sections via $gg$, $qg$, and $q\overline{q}$ initial states are calculated as well as the corresponding spin-spin asymmetries. We find that $χ_1$ production increases relative to direct $ψ$ and $χ_2$ production, providing up to $25\%$ of the observable $e^+e^-$ pairs arising from $ψ$ decays in $pp$ collisions at $\sqrt{s} = 500\,GeV$. The spin-dependence of $χ_1$ production, however, is much smaller than for either direct $ψ$ or $χ_2$ production and so will likely be far less useful than either process in probing the polarized gluon structure function of the proton. A subset of the ${\cal O}(α_S^3)$ radiative corrections to $χ_2$ production involving initial state quarks are also performed and compared to leading order $gg \rightarrow χ_2$ predictions.