Precision Global Determination of the $B\to X_s\gamma$ Decay Rate

Abstract

We perform the first global fit to inclusive $B\to X_s\gamma$ measurements using a model-independent treatment of the nonperturbative $b$-quark distribution function, with next-to-next-to-leading logarithmic resummation and $\mathcal{O}({\alpha }_s^2)$ fixed-order contributions. The normalization of the $B\to X_s\gamma$ decay rate, given by $|C_7^{\mathrm{incl}}{V}_{tb}{V}_{ts}^{\ast }{|}^2$, is sensitive to physics beyond the Standard Model (SM). We determine $|C_7^{\mathrm{incl}}{V}_{tb}{V}_{ts}^{\ast }|=(14.77\pm 0.51_{\mathrm{fit}}\pm 0.59_{\mathrm{theory}}\pm 0.08_{\mathrm{param}})\times 10^{-3}$, in good agreement with the SM prediction, and the $b$-quark mass $m_b^{1S}=(4.750\pm 0.027_{\mathrm{fit}}\pm 0.033_{\mathrm{theory}}\pm 0.003_{\mathrm{param}})\mathrm{GeV}$. Our results suggest that the uncertainties in the extracted $B\to X_s\gamma$ rate have been underestimated by up to a factor of two, leaving more room for beyond-SM contributions.

21 pages, 8 figures

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