Electroweak Radiative Corrections tob→sγ

Two loop electroweak corrections to $b\to s\gamma$ decays are computed. Fermion and photonic loop effects are found to reduce $R\equiv B(b\to s\gamma )/B(b\to \mathrm{ce}\nu )$ by $\sim (8\pm 2)\%$ and lead to the standard model prediction $B(B\to X_s\gamma )=(3.28\pm 0.30)\times {10}^{-4\mathrm{}}$ for inclusive $B$ meson decays. Comparison of $R^{\mathrm{theory}}=(3.04\pm 0.25)\times {10}^{-3\mathrm{}}(1+0.10\rho )$, where $\rho$ is a Wolfenstein Cabibbo-Kobayashi-Maskawa parameter, with the current experimental average $R^{\exp }=(2.52\pm 0.52)\times {10}^{-3\mathrm{}}$ gives $\rho =-1.7\mathrm{}\pm 1.9$ which is consistent with $-0.21\mathrm{}\le \rho \le 0.27$ obtained from other $B$ and $K$ physics constraints.