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

Using a data sample corresponding to an integrated luminosity of $2.0f{b}^{-1}$, 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 $6.5<p_T<14.0\text{ GeV}$. The cross-section for prompt production of ${\eta }_c(1S)$ mesons relative to that of the $J\mathrm{/}\psi$ meson is measured using the $p\bar{p}$ 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 $J\mathrm{/}\psi \to p\bar{p}$ and ${\eta }_c\to p\bar{p}$ decays. The prompt ${\eta }_c(1S)$ production cross-section is determined to be ${\sigma_{\eta_c(1S)} = 1.26 \pm 0.11\pm 0.08 \pm 0.14 ,\mu b}$,wherethelastuncertaintyincludesthatonthe${J/\psi}$mesoncross-section\mathrm{.}Theratioofthebranchingfractionsof$b$-hadron decays to the ${\eta }_c(1S)$ and $J\mathrm{/}\psi$ states is measured to be ${$\mathcal{B}${b\to\eta_c X}/$\mathcal{B}${b\to J/\psi X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the $J\mathrm{/}\psi \to p\bar{p}$ and ${\eta }_c\to p\bar{p}$ decays. The difference between the $J\mathrm{/}\psi$ and ${\eta }_c(1S)$ 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.