We consider the $$ {B}_s^0 $$ B s 0 → μ+μ−γ effective lifetime, and the related CP-phase sensitive quantity $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ , 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 $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ , 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 $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ prediction. For high q2, we find that the corresponding pollution from broad-charmonium resonances has a surprisingly small effect on $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ . 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 $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ behaving like a ratio-of-amplitudes observable. Our study suggests that $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ A ΔΓ s μμγ 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 $$ {B}_s^0 $$ 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.
In recent years, intriguing hints for the violation of lepton flavour universality have accumulated.In particular, deviations from the Standard-Model (SM) predictions in B → D ( * ) τ ν/B → D ( * ) ν, in the anomalous magnetic moment of the muon and in b → s + − data were observed with a significance of > 3 σ, > 4 σ and > 5 σ, respectively. Furthermore, in a recent re-analysis of 2018 Belle data, it was found that the forward-backward asymmetry of B → D * µν vs B → D * eν disagrees with the SM prediction by ≈4 σ which would be an additional sign of lepton flavour universality violation. Since one naturally expects muon-related new effects to also emerge at some point in b → cµν decays, the above putative deviation might share a common origin with the other flavour anomalies. We show that a tensor operator is necessary to significantly improve the global fit w.r.t. the SM, which can only be induced (at tree-level in a renormalizable model) by a scalar leptoquark. Interestingly, among the two possible representations, the SU (2)L-singlet S1 and the doublet S2, which can both also account for the anomalous magnetic moment of the muon, only S1 can provide a good fit as it gives rise to the scenario CV L, CSL = −4CT . While the constraints from (differences of) other angular observables prefer a smaller value of ∆AFB than the current central one, this scenario is significantly preferred (≈ 3σ) over the SM hypothesis, and compatible with constraints such as B → K * νν and electroweak precision bounds.
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