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 $3.0 {\,\mathrm{fb}}^{-1} $ , collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting by ${\mathcal {B}} _C \equiv {\mathcal {B}} ( {{b}} \!\rightarrow C X ) \times {\mathcal {B}} ( C\!\rightarrow \phi \phi )$ the inclusive branching fraction of a ${{b}} $ hadron to a charmonium state C that decays into a pair of $\phi $ mesons, ratios $R^{C_1C_2}\equiv {\mathcal {B}} _{C_1} / {\mathcal {B}} _{C_2}$ are determined as $R^{{\upchi _{{{c}} 0}}}_{{\eta _{{c}}} (1S)} = 0.147 \pm 0.023 \pm 0.011$ , $R^{{\upchi _{{{c}} 1}}}_{{\eta _{{c}}} (1S)} = 0.073 \pm 0.016 \pm 0.006$ , $R^{{\upchi _{{{c}} 2}}}_{{\eta _{{c}}} (1S)} = 0.081 \pm 0.013 \pm 0.005$ , $R^{{\upchi _{{{c}} 1}}}_{{\upchi _{{{c}} 0}}} = 0.50 \pm 0.11 \pm 0.01$ , $R^{{\upchi _{{{c}} 2}}}_{{\upchi _{{{c}} 0}}} = 0.56 \pm 0.10 \pm 0.01$ and $R^{{\eta _{{c}}} (2S)}_{{\eta _{{c}}} (1S)} = 0.040 \pm 0.011 \pm 0.004$ . 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 ${\upchi _{{{c}} 2}} (2P)$ states are obtained as $R^{X(3872){\upchi _{{{c}} 1}}} < 0.34$ , $R^{X(3915){\upchi _{{{c}} 0}}} < 0.12$ and $R^{{\upchi _{{{c}} 2}} (2P)}_{{\upchi _{{{c}} 2}}} < 0.16$ . Differential cross-sections as a function of transverse momentum are measured for the ${\eta _{{c}}} (1S)$ and $\chi _c$ states. The branching fraction of the decay ${{{B}} ^0_{{s}}} \!\rightarrow \phi \phi \phi $ is measured for the first time, ${\mathcal {B}} ( {{{B}} ^0_{{s}}} \!\rightarrow \phi \phi \phi ) = (2.15 \pm 0.54 \pm 0.28 \pm 0.21_{{\mathcal {B}}}) \times 10^{-6}$ . Here the third uncertainty is due to the branching fraction of the decay ${{{B}} ^0_{{s}}} \!\rightarrow \phi \phi $ , which is used for normalization. No evidence for intermediate resonances is seen. A preferentially transverse $\phi $ polarization is observed. The measurements allow the determination of the ratio of the branching fractions for the ${\eta _{{c}}} (1S)$ decays to $\phi \phi $ and ${{p}} {\overline{{{p}}}} $ as ${\mathcal {B}} ( {\eta _{{c}}} (1S)\!\rightarrow \phi \phi )/{\mathcal {B}} ( {\eta _{{c}}} (1S)\!\rightarrow {{p}} {\overline{{{p}}}} ) = 1.79 \pm 0.14\pm 0.32$ .