On the effective lifetime of B s → μμγ

Abstract

Abstract We consider the B s 0 $$ {B}_s^0 $$ → μ + μ − γ effective lifetime, and the related CP-phase sensitive quantity A ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ , 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 ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ , 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 q 2. For low q 2, we show how to shape the integration range in order to reduce the impact of the ϕ-resonance modelling on the A ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ prediction. For high q 2, we find that the corresponding pollution from broad-charmonium resonances has a surprisingly small effect on A ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ . This is due to a number of cancellations, that can be traced back to the complete dominance of semi-leptonic operator contributions for high q 2 — at variance with low q 2 — and to A ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ behaving like a ratio-of-amplitudes observable. Our study suggests that A ΔΓ s μμγ $$ {A}_{{\Delta \Gamma}_s}^{\mu \mu \gamma} $$ is — especially at high q 2 — 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 q 2 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.

Keywords

• CP violation
• Heavy Quark Physics
• Beyond Standard Model