Measurements of the branching fraction ratio $\mathcal{B}(\mathcal{\phi }\to {\mathcal{\mu }}^{+}{\mathcal{\mu }}^{-})\mathcal{/}\mathcal{B}(\mathcal{\phi }\to {\mathcal{e}}^{+}{\mathcal{e}}^{-})$ with charm meson decays

Measurements of the branching fraction ratio $\mathcal{B}(\mathcal{\phi }\to {\mathcal{\mu }}^{+}{\mathcal{\mu }}^{-})\mathcal{/}\mathcal{B}(\mathcal{\phi }\to {\mathcal{e}}^{+}{\mathcal{e}}^{-})$ with $D_s^{+}\to {\pi }^{+}\phi$ and $D^{+}\to {\pi }^{+}\phi$ decays, denoted $R_{\phi \pi }^s$ and $R_{\phi \pi }^d$, are presented. The analysis is performed using a dataset corresponding to an integrated luminosity of 5.4${\mathrm{f}\mathrm{b}}^{-1}$ of $pp$ collision data collected with the LHCb experiment. The branching fractions are normalised with respect to the $B^{+}\to K^{+}J\mathrm{/}\psi (\to e^{+}{e}^{-})$ and $B^{+}\to K^{+}J\mathrm{/}\psi (\to {\mu }^{+}{\mu }^{-})$ decay modes. The combination of the results yields $$R_{\phi \pi }=1.022\pm 0.012(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.048(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})\mathrm{.}$$ The result is compatible with previous measurements of the $\phi \to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ branching fractions and predictions based on the Standard Model.