Study of charmonium production in b-hadron decays and first evidence for the decay B-s(0) -> phi phi phi

Using decays to f-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) x B(C -> 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-C2(C1) = B-C1/B-C2 are determined as R-eta c(1S)(chi c0) = 0.147 +/- 0.023 +/- 0.011, R-eta c(1S)(chi c1) = 0.073 +/- 0.016 +/- 0.006, R-eta c(1S)(chi c2) = 0.081 +/- 0.013 +/- 0.005, R-chi c0(chi c1) = 0.50 +/- 0.11 +/- 0.01, R-chi c0(chi c2) = 0.56 +/- 0.10 +/- 0.01 and R-eta c(1S)(eta c(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.c2(2P) states are obtained as R-chi c1(X(3872)) < 0.34, R-chi c0(X(3915)) < 0.12 and R-chi c2(chi c2(2P)) < 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-s(0). phi phi phi is measured for the first time, B(B-s(0) -> phi phi phi) = (2.15 +/- 0.54 +/- 0.28 +/- 0.21 B) x10(-6). Here the third uncertainty is due to the branching fraction of the decay B-s(0) -> phi phi, which is used for normalization. No evidence for intermediate resonances is seen. A preferentially transverse phi polarization is observed. Themeasurements allow the determination of the ratio of the branching fractions for the eta(c)(1S) decays to ff and p (p) over bar as B(eta(c)(1S) -> phi phi)/B(eta(c)(1S) -> p (p) over bar) = 1.79 +/- 0.14 +/- 0.32.