Abstract
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$fb^{−1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting by $\mathcal{B}_C≡\mathcal{B}(b \to CX)×\mathcal{B}(C \to \phi\phi)$ the inclusive branching fraction of a b hadron to a charmonium state C that decays into a pair of $\phi$ mesons, ratios $R^{C1}_{C2} ≡ \mathcal{B}_{C1}/\mathcal{B}_{C2}$ are determined as $R^{\chi_{c0}}_{\eta_c(1S)} = 0.147 \pm 0.023 \pm 0.011, R^{\chi_{c1}}_{\eta_c(1S)} = 0.073 \pm 0.016 \pm 0.006, R^{\chi_{c2}}_{\eta_c(1S)} = 0.081 \pm 0.013 \pm 0.005, R^{\chi_{c1}}_{\chi_{c0}}=0.50 \pm 0.11 \pm 0.01, R^{\chi_{c2}}_{\chi_{c0}} = 0.56 \pm 0.10 \pm 0.01$ 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 $\chi_{c2}(2P)$ states are obtained as $R^{X(3872)}_{\chi_{c1}} < 0.34$, $R^{X(3915)}_{\chi_{c0}} < 0.12$ and $R^{\chi_{c2}(2P)}_{\chi_{c2}} < 0.16$. 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 $B^0_s \to \phi\phi\phi$ is measured for the first time, $\mathcal{B}(B^0_s \to \phi\phi\phi) = (2.15 \pm 0.54 \pm 0.28 \pm 0.21_{\mathcal{B}})×10^{−6}$. Here the third uncertainty is due to the branching fraction of the decay $B^0_s \to \phi\phi\phi$, 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 $\mathcal{B}(\eta_c(1S) \to \phi\phi)/\mathcal{B}(\eta_c(1S)→p\overline{p}) = 1.79 \pm 0.14 \pm 0.32$.
LHCb Collaboration