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Insights on the current semi-leptonic $B$-decay discrepancies -- and how $B_s \to \mu^+ \mu^- \gamma$ can help

Authors :
Guadagnoli, Diego
Normand, Camille
Simula, Silvano
Vittorio, Ludovico
Source :
J. High Energ. Phys. 2023, 102 (2023)
Publication Year :
2023

Abstract

$B_s \to \mu^+ \mu^- \gamma$, measured at high $q^2$ as a partially reconstructed decay, can probe the origin of the existing discrepancies in semi-leptonic $b \to s$ and $b \to c$ 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, $B_s \to \mu^+ \mu^- \gamma$ 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 $q^2$. After quantifying to the best of our knowledge the $B_s \to \mu^+ \mu^- \gamma$ experimental over the long haul, we infer the $B_s \to \mu^+ \mu^- \gamma$ sensitivity to the couplings relevant to the anomalies. In the example of the real-$\delta C_{9,10}$ scenario, we find significances below 3$\sigma$. 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 $q^2$, and not affected by long-distance issues such as narrow resonances or intermediate charmed di-meson rescattering.<br />Comment: 29 pages, 8 figures, 2 tables

Details

Database :
arXiv
Journal :
J. High Energ. Phys. 2023, 102 (2023)
Publication Type :
Report
Accession number :
edsarx.2308.00034
Document Type :
Working Paper
Full Text :
https://doi.org/10.1007/JHEP10(2023)102