Item

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