Study of Charmonium Production in b-Hadron Decays and First Evidence for the Decay B0s → ϕ ϕ ϕ

Using decays to ϕ-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 fb^−1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting by B_C ≡ B(b → CX) × B(C → ϕϕ) the inclusive branching fraction of a b hadron to a charmonium state C that decays into a pair of ϕ mesons, ratios R_C2^C1 ≡ B_{C_1}/B_{C_2} are determined as R_{ηc(1S)}^{χc0} = 0.147 ± 0.023 ± 0.011, R_{ηc(1S)}^{χc1} = 0.073 ± 0.016 ± 0.006, R_{ηc(1S)}^{χc2} = 0.081 ± 0.013 ± 0.005, R_{χc0}^{χc1} = 0.50 ± 0.11 ± 0.01, R_{χc0}^{χc2} = 0.56 ± 0.10 ± 0.01 and R_{ηc(1S)}^{ηc(2S)} = 0.040 ± 0.011 ± 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 χc2(2P) states are obtained as R_{χc1}^{X(3872)} < 0.34, R_{χc0}^{X(3915)} < 0.12 and R_{χc2}^{χc2(2P)} < 0.16. Differential cross-sections as a function of transverse momentum are measured for the η_c(1S) and χ_c states. The branching fraction of the decay B0s → ϕ ϕ ϕ is measured for the first time, B(B0s → ϕ ϕ ϕ) = (2.15 ± 0.54 ± 0.28 ± 0.21_B) × 10^−6. Here the third uncertainty is due to the branching fraction of the decay B0s → ϕ ϕ, which is used for normalization. No evidence for intermediate resonances is seen. A preferentially transverse ϕ polarization is observed. The measurements allow the determination of the ratio of the branching fractions for the η_c(1S) decays to ϕ ϕ and p anti-p as B(η_c(1S) → ϕ ϕ)/B(ηc(1S) → p anti-p) = 1.79 ± 0.14 ± 0.32.