Study of charmonium production in ${b}$-hadron decays and first evidence for the decay ${{{B}} ^0_{{s}}} \!\rightarrow \phi \phi \phi $

Using decays to $\phi$-meson pairs, the inclusive production of charmonium states in $b$-hadron decays is studied with $pp$ collision data corresponding to an integrated luminosity of $3.0fb^{-1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting by $B_C\equiv B(b\to CX)\times B(C\to\phi\phi)$ the inclusive branching fraction of a $b$ hadron to a charmonium state $C$ that decays into a pair of $\phi$ mesons, ratios $R^{C1}_{C2}\equiv B_{C1}/B_{C2}$ are determined as $R^{\chi_{c0}}_{\eta_c(1S)}=0.147\pm0.023\pm0.011$, $R^{\chi_{c1}}_{\eta_c (1S)}=0.073\pm0.016\pm0.006$, $R^{\chi_{c2}}_{\eta_c (1S)}=0.081\pm0.013\pm0.005$, $R^{\chi_{c1}}_{\chi_{c0}}=0.50\pm0.11\pm0.01$, $R^{\chi_{c2}}_{\chi_{c0}}=0.56\pm0.10\pm0.01$ and $R^{\eta_c (2S)}_{\eta_c(1S)}=0.040\pm0.011\pm0.004$. Here and below the first uncertainties are statistical and the second systematic. Upper limits at $90\%$ confidence level for the inclusive production of $X(3872)$, $X(3915)$ and $\chi_{c2}(2P)$ states are obtained as $R^{X(3872)}_{\chi_{c1}}