Measurement of the $η_c(1S)$ production cross-section in $pp$ collisions at $\sqrt{s} = 13$ TeV

Using a data sample corresponding to an integrated luminosity of $2.0\,fb^{-1}$, collected by the LHCb experiment, the production of the $η_c(1S)$ 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 ${6.5 < p_{T} < 14.0\text{ GeV}}$. The cross-section for prompt production of $η_c(1S)$ mesons relative to that of the $J/ψ$ meson is measured using the ${p\bar{p}}$ decay mode and is found to be ${σ_{η_c(1S)}/σ_{J/ψ} = 1.69 \pm 0.15 \pm 0.10 \pm 0.18}$. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the ${J/ψ\to p \bar{p}}$ and ${η_c\to p \bar{p}}$ decays. The prompt $η_c(1S)$ production cross-section is determined to be ${σ_{η_c(1S)} = 1.26 \pm 0.11\pm 0.08 \pm 0.14 \,μb}$, where the last uncertainty includes that on the ${J/ψ}$ meson cross-section. The ratio of the branching fractions of $b$-hadron decays to the $η_c(1S)$ and ${J/ψ}$ states is measured to be ${\mathcal{B}_{b\toη_c X}/\mathcal{B}_{b\to J/ψX} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the ${J/ψ\to p \bar{p}}$ and ${η_c\to p \bar{p}}$ decays. The difference between the ${J/ψ}$ and $η_c(1S)$ masses is also determined to be ${113.0 \pm 0.7 \pm 0.1\text{ MeV}}$, which is the most precise single measurement of this quantity to date.