Using a data sample corresponding to an integrated luminosity of $2.0,fb^{-1}$, collected by the LHCb experiment, the production of the $eta_c(1S)$ state in proton-proton collisions at a centre-of-mass energy of $sqrt{s}=13 text{ TeV}$ is studied in the rapidity range ${2.0 < y < 4.5}$ and in the transverse momentum range ${6.5 < p_{T} < 14.0text{ GeV}}$. The cross-section for prompt production of $eta_c(1S)$ mesons relative to that of the $J/psi$ meson is measured using the ${pbar{p}}$ decay mode and is found to be ${sigma_{eta_c(1S)}/sigma_{J/psi} = 1.69 pm 0.15 pm 0.10 pm 0.18}$. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the ${J/psito p bar{p}}$ and ${eta_cto p bar{p}}$ decays. The prompt $eta_c(1S)$ production cross-section is determined to be ${sigma_{eta_c(1S)} = 1.26 pm 0.11pm 0.08 pm 0.14 ,mu b}$, where the last uncertainty includes that on the ${J/psi}$ meson cross-section. The ratio of the branching fractions of $b$-hadron decays to the $eta_c(1S)$ and ${J/psi}$ states is measured to be ${mathcal{B}_{btoeta_c X}/mathcal{B}_{bto J/psi X} = 0.48 pm 0.03 pm 0.03 pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the ${J/psi to p bar{p}}$ and ${eta_cto p bar{p}}$ decays. The difference between the ${J/psi}$ and $eta_c(1S)$ masses is also determined to be ${113.0 pm 0.7 pm 0.1text{ MeV}}$, which is the most precise single measurement of this quantity to date.
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