Analysis of neutral $B$-meson decays into two muons

Branching fraction and effective lifetime measurements of the rare decay $B^0_s\toμ^+μ^-$ and searches for the decays $B^0\toμ^+μ^-$ and $B^0_s\toμ^+μ^-γ$ are reported using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of $7$ TeV, $8$ TeV and $13$ TeV, corresponding to a luminosity of $9$ fb$^{-1}$. The branching fraction ${\mathcal{B}}(B^0_s\toμ^+μ^-)=\left(3.09^{+0.46+0.15}_{-0.43-0.11}\right)\times 10^{-9}$ and the effective lifetime $τ(B^0_s\toμ^+μ^-)=(2.07\pm 0.29\pm 0.03)$ are measured, where the first uncertainty is statistical and the second systematic. No significant signal for $B^0\toμ^+μ^-$ and $B^0_s\toμ^+μ^-γ$ decays is found and upper limits $\mathcal{B}(B^0\toμ^+μ^-)<2.6\times 10^{-10}$ and $\mathcal{B}(B^0_s\toμ^+μ^-γ)<2.0\times 10^{-9}$ at the 95% CL are determined, where the latter is limited to the range $m_{μμ} > 4.9$ GeV$/c^2$. The results are in agreement with the Standard Model expectations.