The inclusive $\bar B \to X_s \gamma$ decay rate with higher precision

Abstract

We present a new and upgraded analysis of the inclusive weak radiative decay of the $B$ meson in the standard model and beyond. The ${\mathcal O}(\alpha_s)$ perturbative corrections are included in a formally complete manner. At the order $\alpha_s^2$, exact dependence on the charm quark mass is calculated for the dominant corrections, which removes a sizeable uncertainty that was present in all the previous analyses. The global normalization factor and many of the non-perturbative contributions are expressed in terms of the kinetic-scheme mass of the $b$-quark and the heavy-quark-expansion matrix elements. These parameters are adopted from the most recent semileptonic fits that include ${\mathcal O}(\alpha_s^3)$ corrections and up-to-date experimental results. We find ${\mathcal B}_{s\gamma}^{\rm SM} = (3.54 \pm 0.14)\times 10^{-4}$ for the CP- and isospin-averaged branching ratio of the considered decay in the standard model, with a lower cut on the photon energy $E_\gamma > 1.6\,{\rm GeV}$. It agrees with the current experimental average ${\mathcal B}_{s\gamma}^{\rm exp} = (3.49 \pm 0.19)\times 10^{-4}$, which provides constraints on beyond standard model physics. In particular, we find $M_{H^\pm} > 670\,{\rm GeV}$ at $95\%\,{\rm C.L.}$ for the charged Higgs boson mass in the two-Higgs-doublet model~II.