Measurement of $J/\psi$ and $\psi\left(2S\right)$ production in $p+p$ and $p+d$ interactions at 120 GeV

We report the $p+p$ and $p+d$ differential cross sections measured in the SeaQuest experiment for $J/\psi$ and $\psi\left(2S\right)$ production at 120 GeV beam energy covering the forward $x$-Feynman ($x_F$) range of $0.5 < x_F <0.9$. The measured cross sections are in good agreement with theoretical calculations based on the nonrelativistic QCD (NRQCD) using the long-distance matrix elements deduced from a recent global analysis of proton- and pion-induced charmonium production data. The $\sigma_{\psi\left(2S\right)} / \sigma_{J/\psi}$ cross section ratios are found to increase as $x_F$ increases, indicating that the $q \bar{q}$ annihilation process has larger contributions in the $\psi\left(2S\right)$ production than the $J/\psi$ production. The $\sigma_{pd}/2\sigma_{pp}$ cross section ratios are observed to be significantly different for the Drell-Yan process and $J/\psi$ production, reflecting their different production mechanisms. We find that the $\sigma_{pd}/2\sigma_{pp}$ ratios for $J/\psi$ production at the forward $x_F$ region are sensitive to the $\bar{d}/ \bar{u}$ flavor asymmetry of the proton sea, analogous to the Drell-Yan process. The transverse momentum ($p_T$) distributions for $J/\psi$ and $\psi\left(2S\right)$ production are also presented and compared with data collected at higher center-of-mass energies.