Targeting (Pseudo)-Scalar CP Violation with $B_s \to \mu^+\mu^-$

The leptonic decay $B_s \to \mu^+\mu^-$ is both rare and theoretically clean, making it an excellent probe for New Physics searches. Due to its helicity suppression in the Standard Model, this decay is particularly sensitive to new (pseudo)-scalar contributions. We present a new strategy for detecting CP-violating New Physics contributions of this kind, exploiting two observables: $\mathcal{A}_{\Delta\Gamma_s}^{\mu\mu}$, which is accessible due to the sizeable decay width difference of the $B_s$ system, and the mixing-induced CP asymmetry $\mathcal{S}_{\mu\mu}$. The strategy also uses information from $B\to K^{(*)} \mu^+\mu^-$ and $B_s\to \phi \mu^+\mu^-$ decays. We find remarkably constrained regions in the $\mathcal{A}_{\Delta\Gamma_s}^{\mu\mu}$-$\mathcal{S}_{\mu\mu}$ plane that serve as promising targets for future measurements.