Measurement of CP violation in the $B_s^0\to \varphi \varphi$ decay and search for the $B^0\to \varphi \varphi$ decay

A measurement of the time-dependent CP-violating asymmetry in $B_s^0\to \varphi \varphi$ decays is presented. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $5.0$fb${}^{-1}$ collected by the $LHCb$ experiment at centre-of-mass energies $\sqrt{s} = 7$ TeV in 2011, 8 TeV in 2012 and 13 TeV in 2015 and 2016, a signal yield of around 9000 $B_s^0\to \varphi \varphi$ decays is obtained. The CP-violating phase ${\varphi }_s^{s\bar{s}s}$ is measured to be $-0.073\pm 0.115$(stat)$\pm 0.027$(syst)rad,undertheassumptionitisindependentonthehelicityofthe$\phi\phi$ decay. In addition, the CP-violating phases of the transverse polarisations under the assumption of CP conservation of the longitudinal phase are measured. The helicity-independent direct CP-violation parameter is also measured, and is found to be $\mathrm{\mid }\lambda \mathrm{\mid }=0.99\pm 0.05$(stat)$\pm 0.01$(syst). In addition, $T$-odd triple-product asymmetries are measured. The results obtained are consistent with the hypothesis of CP conservation in $b\to \bar{s}s\bar{s}$ transitions. Finally, a limit on the branching fraction of the $B^0\to \varphi \varphi$ decay is determined to be $\mathcal{B}(B^0\to \varphi \varphi )<2.7\times {10}^{-8}$ at 90% confidence level.