Phenomenological NLO analysis of η_c production at the LHC in the collider and fixed-target modes

In view of the good agreement between the LHCb prompt-${\eta }_c$ data at $\sqrt{s}=7$ and 8 TeV and the NLO colour-singlet model predictions –i.e. the leading $v^2$ NRQCD contribution–, we provide predictions in the LHCb acceptance for the forthcoming 13 TeV analysis bearing on data taken during the LHC Run2. We also provide predictions for $\sqrt{s}=115$ GeV for proton-hydrogen collisions in the fixed-target mode which could be studied during the LHC Run3. Our predictions are complemented by a full theoretical uncertainty analysis. In addition to cross section predictions, we elaborate on the uncertainties on the $p\overline{p}$ branching ratio –necessary for data-theory comparison– and discuss other usable branching fractions for future studies.