Evidence for the decays $B^0\to {\bar{D}}^{(\ast )0}\phi$ and updated measurements of the branching fractions of the $B_s^0\to {\bar{D}}^{(\ast )0}\phi$ decays

Evidence for the decays $B^0\to {\bar{D}}^0\phi$ and $B^0\to {\bar{D}}^{\ast 0}\phi$ is reported with a significance of 3.6$\sigma$ and 4.3$\sigma$, respectively. The analysis employs $pp$ collision data at centre-of-mass energies $\sqrt{s}=7$, 8 and 13 TeV collected by the LHCb detector and corresponding to an integrated luminosity of 9 ${\mathrm{f}\mathrm{b}}^{-1}$. The branching fractions are measured to be $\mathcal{B}(B^0\to {\bar{D}}^0\phi )=(7.7\pm 2.1\pm 0.7\pm 0.7)\times {10}^{-7}$,$\mathcal{B}(B^0\to {\bar{D}}^{\ast 0}\phi )=(2.2\pm 0.5\pm 0.2\pm 0.2)\times {10}^{-6}$. In these results, the first uncertainties are statistical, the second systematic, and the third is related to the branching fraction of the $B^0\to {\bar{D}}^0{K}^{+}{K}^{-}$ decay, used for normalisation. By combining the branching fractions of the decays $B^0\to {\bar{D}}^{(\ast )0}\phi$ and $B^0\to {\bar{D}}^{(\ast )0}\omega$, the $\omega$-$\phi$ mixing angle $\delta$ is constrained to be ${\tan }^2\delta =(3.6\pm 0.7\pm 0.4)\times {10}^{-3}$, where the first uncertainty is statistical and the second systematic. An updated measurement of the branching fractions of the $B_s^0\to {\bar{D}}^{(\ast )0}\phi$ decays, which can be used to determine the CKM angle $\gamma$, leads to $\mathcal{B}(B_s^0\to {\bar{D}}^0\phi )=(2.30\pm 0.10\pm 0.11\pm 0.20)\times {10}^{-5}$,$\mathcal{B}(B_s^0\to {\bar{D}}^{\ast 0}\phi )=(3.17\pm 0.16\pm 0.17\pm 0.27)\times {10}^{-5}$.