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

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 $$R^{C_1}_{C_2}\equiv {\mathcal {B}} _{C_1} / {\mathcal {B}} _{C_2}$$ 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 $${\mathcal {B}} ( {\eta _{{c}}} (1S)\!\rightarrow \phi \phi )/{\mathcal {B}} ( {\eta _{{c}}} (1S)\!\rightarrow {{p}} {\overline{{{p}}}} ) = 1.79 \pm 0.14\pm 0.32$$ .