Insights on the current semi-leptonic B-decay discrepancies — and how Bs → μ+μ−γ can help

B s → μ+μ−γ, measured at high q2 as a partially reconstructed decay, can probe the origin of the existing discrepancies in semi-leptonic b → s and b → c decays. We perform a complete study of this possibility. We start by reassessing the alleged discrepancies, with a focus on a unified EFT description. Using the SMEFT, we find that the tauonic Wilson coefficient required by R(D(*)) implies a universal muonic Wilson coefficient of precisely the size required by semi-muonic BR data and, separately, by semi-muonic angular analyses. We thus identify reference scenarios. Importantly, Bs → μ+μ−γ offers a strategy to access them without being affected by the long-distance issues that hamper the prediction of semi-leptonic B decays at low q2. After quantifying to the best of our knowledge the Bs → μ+μ−γ experimental over the long haul, we infer the Bs → μ+μ−γ sensitivity to the couplings relevant to the anomalies. In the example of the real-δC9,10 scenario, we find significances below 3σ. Such figure is to be compared with other single-observable sensitivities that one can expect from e.g. BR and angular data, whether at low or high q2, and not affected by long-distance issues such as narrow resonances or intermediate charmed di-meson rescattering.