$B \to X_s gamma$ in the Standard Model

We give a summary about the various contributions which have to be calculated in order to obtain the next-to-leading logarithmic result for the branching ratio $BR(B \to X_s γ)$. Combining all these ingredients, which were obtained by different groups, a complete next-to-leading-logarithmic prediction of the inclusive decay rate was recently presented in the literature. The theoretical uncertainty in the partonic decay rate is now at the 10% level, i.e., less than half of the error in the previous leading-logarithmic result. We also mention the impact of non-perturbative corrections which scale like $1/m_b^2$ and discuss in some more detail the recently discovered corrections which scale like $1/m_c^2$. It turns out that the $1/m_b^2$- and the $1/m_c^2$ terms lead to corrections to the branching ratio $BR(B \to X_s γ)$ well below the 10% level.

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