Investigating charmonium production at the LHC with the p(p)over-bar final state

We propose to investigate various charmonium states using their common decay channel to p (p) over bar at LHC. Having the branching ratios for charmonium decaying into the p (p) over bar final state measured or calculated, we propose to measure the charmonium production rate for both hadroproduction, including soft-diffraction, and inclusive production from b-hadron decays. We discuss the theoretical impacts in QCD of measuring different charmonium production rates and also the experimental prospects at LHCb, in particular, those for yet unmeasured eta(c) and h(c).