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 $\lvert C_7^{\rm incl} V_{tb} V_{ts}^*\rvert^2$, is sensitive to physics beyond the Standard Model (SM). We determine $\lvert C_7^{\rm incl} V_{tb} V_{ts}^* \rvert = (14.77 \pm 0.51_{\rm fit} \pm 0.59_{\rm theory} \pm 0.08_{\rm param})\times 10^{-3}$, in good agreement with the SM prediction, and the $b$-quark mass $m_b^{1S} = (4.750 \pm 0.027_{\rm fit} \pm 0.033_{\rm theory} \pm 0.003_{\rm param})\,\mathrm{GeV}$. 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.