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

The inclusive production of the $η_c(1S)$, $η_c(2S)$ and $χ_{c}$ 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 $φφ$ pairs. The production branching fractions of the $χ_{c}(1P)$ states in $b$-hadron decays are measured, using $b \to η_c(1S) (\to φφ) X$ 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 $η_c(2S)$ times the branching fraction of its decay into $φφ$ is measured as ${\cal{B}} (b \to η_c(2S) X) \times {\cal{B}} (η_c(2S) \to φφ) = (4.0 \pm 0.6 \pm 0.6 \pm 1.1) \times 10^{-7}$. Furthermore, the mass of the $η_c(1S)$ state is measured to be $M_{η_c(1S)} = 2984.1 \pm 0.5 \pm 0.5$ MeV with the best precision to date.