On the effective lifetime of Bs\u2192 \u03bc\u03bc\u03b3

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We consider the {B}_s^0 → μ+μ−γ effective lifetime, and the related CP-phase sensitive quantity {A}_{{Delta Gamma}_s}^{mu mu gamma} , as a way to obtain qualitatively new insights on the current B-decay discrepancies. Through a fit comparing pre- to post-Moriond-2021 data we identify a few theory benchmark scenarios addressing these discrepancies, and featuring large CP violation in addition. We then explore the possibility of telling apart these scenarios with {A}_{{Delta Gamma}_s}^{mu mu gamma} , once resonance-modeling and form-factor uncertainties are taken into account. We do so in both regions of low and high invariant di-lepton mass-squared q2. For low q2, we show how to shape the integration range in order to reduce the impact of the ϕ-resonance modelling on the {A}_{{Delta Gamma}_s}^{mu mu gamma} prediction. For high q2, we find that the corresponding pollution from broad-charmonium resonances has a surprisingly small effect on {A}_{{Delta Gamma}_s}^{mu mu gamma} . This is due to a number of cancellations, that can be traced back to the complete dominance of semi-leptonic operator contributions for high q2 — at variance with low q2 — and to {A}_{{Delta Gamma}_s}^{mu mu gamma} behaving like a ratio-of-amplitudes observable. Our study suggests that {A}_{{Delta Gamma}_s}^{mu mu gamma} is — especially at high q2 — a potentially valuable probe of short-distance CP-violating effects in the very same Wilson coefficients that are associated to current b → s discrepancies. Its discriminating power, however, relies on progress in form-factor uncertainties. Interestingly, high q2 is the region where {B}_s^0 → μ+μ−γ is already being accessed experimentally, and the region where form factors are more accessible through non-perturbative QCD methods.