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 ${\mathcal{B}}_{s\gamma }^{\mathrm{SM}}=(3.54\pm 0.14)\times 10^{-4}$ for the CP- and isospin-averaged branching ratio of the considered decay in the standard model, with a lower cut on the photon energy $E_{\gamma }>1.6\mathrm{GeV}$. It agrees with the current experimental average ${\mathcal{B}}_{s\gamma }^{\exp }=(3.49\pm 0.19)\times 10^{-4}$, which provides constraints on beyond standard model physics. In particular, we find $M_{H^{\pm }}>670\mathrm{GeV}$ at $95\%C.L.$ for the charged Higgs boson mass in the two-Higgs-doublet model~II.

5 pages, 3 figures