Next-To-Leading Order Differential Cross-Sections for $J/\psi$, $\psi(2S)$ and $\Upsilon$ Production in Proton-Proton Collisions at a Fixed-Target Experiment using the LHC Beams (AFTER@LHC)

Using nonrelativistic QCD (NRQCD) factorization, we calculate the yields for $J/\psi$, $\psi(2S)$ and $\Upsilon(1S)$ hadroproduction at $\sqrt{s}=$ 72 GeV and 115 GeV including the next-to-leading order QCD corrections. Both these center-of-mass energies correspond to those obtained with 7~TeV and 2.76~TeV nucleon beam impinging a fixed target. We study the cross section integrated in $p_t$ as a function of the rapidity as well as the $p_t$ differential cross section in the central rapidity region. Using different NLO fit results of the NRQCD long-distance matrix elements, we evaluate a theoretical uncertainty which is certainly much larger than the projected experimental uncertainties with the expected 20 fb$^{-1}$ to be collected per year with AFTER@LHC.