Measurement of inclusive production of charmonium states in $b$-hadron decays via their decay into $\phi \phi$

The inclusive production of the ${\eta }_c(1S)$, ${\eta }_c(2S)$ and ${\chi }_c$ charmonium states in $b$-hadron decays is studied with LHCb Run~2 data, corresponding to an integrated luminosity of $5.9{\text{fb}}^{-1}$, using charmonia decays to $\phi \phi$ pairs. The production branching fractions of the ${\chi }_c(1P)$ states in $b$-hadron decays are measured, using $b\to {\eta }_c(1S)(\to \phi \phi )X$ as a normalisation channel, with $X$ indicating any additional particles. The results are \begin{align*} &{\cal{B}} (b \to χ_{c0} X) = (1.34 \pm 0.13 \pm 0.06 \pm 0.37) \times 10^{-3}, &{\cal{B}} (b \to χ_{c1} X) = (1.58 \pm 0.12 \pm 0.09 \pm 0.44) \times 10^{-3}, &{\cal{B}} (b \to χ_{c2} X) = (0.55 \pm 0.08 \pm 0.05 \pm 0.15) \times 10^{-3}, \end{align*} where the first uncertainty is statistical, the second systematic and the last is due to the limited knowledge of externally measured branching fractions. The production branching fraction of ${\eta }_c(2S)$ times the branching fraction of its decay into $\phi \phi$ is measured as $\mathcal{B}(b\to {\eta }_c(2S)X)\times \mathcal{B}({\eta }_c(2S)\to \phi \phi )=(4.0\pm 0.6\pm 0.6\pm 1.1)\times {10}^{-7}$. Furthermore, the mass of the ${\eta }_c(1S)$ state is measured to be $M_{{\eta }_c(1S)}=2984.1\pm 0.5\pm 0.5$ MeV with the best precision to date.