CP Violation in Leptonic Rare $B^0_s$ Decays as a Probe of New Physics

The decay $B^0_s\to\mu^+\mu^-$ is a key probe for the search of physics beyond the Standard Model. While the current measurements of the corresponding branching ratio agree with the Standard Model within the uncertainties, significant New-Physics effects may still be hiding in $B^0_s\to\mu^+\mu^-$. In order to reveal them, the observable $\mathcal{A}^{\mu\mu}_{\Delta \Gamma_s}$, which is provided by the decay width difference $\Delta\Gamma_s$ of the $B^0_s$-meson system, plays a central role. We point out that a measurement of a CP-violating observable ${\cal S}_{\rm \mu\mu}$, which is induced through interference between $B^0_s$-$\bar B^0_s$ mixing and $B_s\to\mu^+\mu^-$ decay processes, is essential to obtain the full picture, in particular to establish new scalar contributions and CP-violating phases. We illustrate these findings with future scenarios for the upgrade(s) of the LHC, exploiting also relations which emerge within an effective field theory description of the Standard Model, complemented with New Physics entering significantly beyond the electroweak scale.