Measurement of the production cross-section in collisions at

Using a data sample corresponding to an integrated luminosity of 2.0 $$\, \text {fb} ^{-1}$$, 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 $$6.5< p_{\mathrm {T}} < 14.0 \, \text {GeV} $$. The cross-section for prompt production of $${\eta _{c}} (1S)$$ mesons relative to that of the $${J /\psi }$$ meson is measured using the $$p $$ $$\overline{{p}}$$ 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 $${{J /\psi }} \!\rightarrow {p} {\overline{{p}}} $$ and $${\eta _{c}} \!\rightarrow {p} {\overline{{p}}} $$ decays. The prompt $${\eta _{c}} (1S)$$ production cross-section is determined to be $${\sigma _{{\eta _{c}} (1S)} = 1.26 \pm 0.11\pm 0.08\pm 0.14 \,\upmu \text {b}}$$, 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 $${{\mathcal {B}} _{{b} \!\rightarrow {\eta _{c}} X}/{\mathcal {B}} _{{b} \!\rightarrow {{J /\psi }} X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$$, where the last uncertainty is due to those on the branching fractions of the $${{J /\psi }} \!\rightarrow {p} {\overline{{p}}} $$ and $${\eta _{c}} \!\rightarrow {p} {\overline{{p}}} $$ decays. The difference between the $${J /\psi }$$ and $${\eta _{c}} (1S)$$ masses is also determined to be $$113.0 \pm 0.7 \pm 0.1 \, \text {MeV} $$, which is the most precise single measurement of this quantity to date.