Study of charmonium production in $b$-hadron decays and first evidence for the decay $B_s^0 \rightarrow φφφ$

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 $3.0fb^{-1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting by $B_C\equiv B(b\to CX)\times B(C\toφφ)$ the inclusive branching fraction of a $b$ hadron to a charmonium state $C$ that decays into a pair of $φ$ mesons, ratios $R^{C1}_{C2}\equiv B_{C1}/B_{C2}$ are determined as $R^{χ_{c0}}_{η_c(1S)}=0.147\pm0.023\pm0.011$, $R^{χ_{c1}}_{η_c (1S)}=0.073\pm0.016\pm0.006$, $R^{χ_{c2}}_{η_c (1S)}=0.081\pm0.013\pm0.005$, $R^{χ_{c1}}_{χ_{c0}}=0.50\pm0.11\pm0.01$, $R^{χ_{c2}}_{χ_{c0}}=0.56\pm0.10\pm0.01$ and $R^{η_c (2S)}_{η_c(1S)}=0.040\pm0.011\pm0.004$. 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 $χ_{c2}(2P)$ states are obtained as $R^{X(3872)}_{χ_{c1}}<0.34$, $R^{X(3915)}_{χ_{c0}}<0.12$ and $R^{χ_{c2}(2P)}_{χ_{c2}}<0.16$. 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 $B_s^0\rightarrowφφφ$ is measured for the first time, $B(B_s^0\toφφφ)=(2.15\pm0.54\pm0.28\pm0.21_{B})\times 10^{-6}$. Here the third uncertainty is due to the branching fraction of the decay $B_s^0\toφφ$, 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 $φφ$ and $p\bar{p}$ as $B(η_c(1S)\toφφ)/B(η_c(1S)\to p\bar{p})=1.79\pm0.14\pm0.32$.