$\bar{B}\to X_s \gamma$ in the Two Higgs Doublet Model up to Next-to-Next-to-Leading Order in QCD

Understand

We compute three-loop matching corrections to the Wilson coefficients $C_7$ and $C_8$ in the Two Higgs Doublet Model by applying expansions for small, intermediate and large charged Higgs boson masses.

• The results are used to evaluate the branching ratio of $\bar{B}\to X_s \gamma$ to next-to-next-to leading order accuracy, and to determine an updated lower limit on the charged Higgs boson mass.
• We find $\mhplus \ge 380 $GeV at 95% confidence level when the recently completed BABAR data analysis is taken into account.
• Our results for the charged Higgs contribution to the branching ratio exhibit considerably weaker sensitivity to the matching scale $\mu_0$, as compared to previous calculations.