A search for the very rare $B^{ *0}\to\mu^+\mu^-$ and $B_{ s}^{ *0}\to\mu^+\mu^-$ decays is conducted by analysing the $B_c^+\to \pi^+\mu^+\mu^-$ process. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9$\text{ \,fb}^{ -1}$. The signal signatures correspond to simultaneous peaks in the $\mu^+\mu^-$ and $\pi^+\mu^+\mu^-$ invariant masses. No evidence for an excess of events over background is observed for either signal decay mode. Upper limits at the $90\%$ confidence level are set on the branching fractions relative to that for $B_c^+\to J\mskip -3mu/\mskip -2mu\psi\pi^+$ decays, \begin{ equation*} { \cal R}_{ B^{ *0}(\mu^+\mu^-)\pi^+/J\mskip -3mu/\mskip -2mu\psi\pi^+} < 3.8\times 10^{ -5}\ \text{ and }\: { \cal R}_{ B_{ s}^{ *0}(\mu^+\mu^-)\pi^+/J\mskip -3mu/\mskip -2mu\psi\pi^+} < 5.0\times 10^{ -5}\,. \end{ equation*}
Categories: hep-ex