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

A measurement of the time-dependent $CP$-violating asymmetry in $B_s^0 \to \phi\phi$ decays is presented, along with measurements of the $T$-odd triple-product asymmetries. Using a sample of proton-proton collision data corresponding to an integrated luminosity of $5.0 fb^{-1}$ collected with the LHCb detector, a signal yield of approximately 8500 $B_s^0 \to \phi\phi$ decays is obtained. The $CP$-violating phase is measured to be ${\phi_s=-0.07\pm0.13{\rm stat.}\pm0.03{\rm syst.}}{\rm rad}$. The triple-product asymmetries are measured to be ${A_U=0.000\pm0.012{\rm stat.}\pm0.004 {\rm syst.}}$ and ${A_V=-0.003\pm0.012{\rm stat.}\pm0.004{\rm syst.}}$. The results obtained are consistent with the hypothesis of $CP$ conservation in $b\to s\overline{s}s$ transitions. In addition, an improved limit on the branching fraction of the $B^0\to\phi\phi$ decay is set, $\mathcal{B}(B^0\to\phi\phi)<2.4\times 10^{-8}$ at 90 % confidence level.