Measurement of rare $B \to \mu^+\mu^-$ decays with the Phase-2 upgraded CMS detector at the HL-LHC

The sensitivity of the upgraded CMS detector for measuring the rare decays $B_{s}^0\to \mu^+ \mu^-$ and $B^0\to \mu^+ \mu^-$ in the HL-LHC scenario is studied. The upgraded detector, especially with its improved momentum resolution, and the foreseen total integrated luminosity of $3000~\mathrm{fb}^{-1}$ are expected to enable high precision measurements of the branching fractions of $B_{s}^0\to \mu^+ \mu^-$ and the effective lifetime of the $B_{s}^0\to \mu^+ \mu^-$ decay with reduced systematic and statistical uncertainties. At $3000~\mathrm{fb}^{-1}$, it will also be possible to observe the $B^0\to \mu^+ \mu^-$ decay with more than 5$\sigma$ significance.