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The rare decays $B_{s(d)} \to \mu^+\mu^-$ play a key role for the testing ofthe Standard Model. An overview of the most recent theoretical predictions ofthe corresponding branching ratios is given, emphasizing that the sizable decaywidth difference $\Delta\Gamma_s$ of the $B_s$-meson system affects the $B_s\to\mu^+\mu^-$ channel. As a consequence, the calculated Standard Model branchingratio has to be upscaled by about 10% to BR$(B_s\to\mu^+\mu^-)=(3.54\pm0.30)\times 10^{-9}$. This prediction is the referencevalue for the comparison with the time-integrated experimental branching ratio,where LHCb has recently reported $(3.2^{+1.5}_{-1.2})\times10^{-9}$corresponding to the first evidence for $B_s\to \mu^+\mu^-$. The$\Delta\Gamma_s$ effects have also to be included in the constraints on theparameter space of New-Physics models following from the experimental data.Furthermore, $\Delta\Gamma_s$ makes a new observable through the effective$B_s\to \mu^+\mu^-$ lifetime accessible, which probes New Physics in a waycomplementary to the branching ratio and adds an exciting new topic to theagenda for the high-luminosity upgrade of the LHC.

Theory News on $B_{s(d)} \to \mu^+\mu^-$ Decays