$ \overline{B}\ \to {X_s}\gamma $ in the Two Higgs Doublet Model up to next-to-next-to-leading order in QCD

Thomas Hermann,Mikolaj Misiak,Matthias Steinhauser

doi:10.1007/jhep11(2012)036

Thomas Hermann, Mikolaj Misiak + Show 1 more

Open Access

https://doi.org/10.1007/jhep11(2012)036

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Abstract

Abstract 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 $ \overline{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 M H+ ≥ 380GeV 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 μ 0, as compared to previous calculations.

Highlights

The outline of the paper is as follows: we discuss the matching coefficients up to the three-loop order
The constraint has been derived using only the Next-to-Leading Order (NLO) expressions for the 2HDM contributions at the electroweak scale, while the SM contributions were treated at the NNLO [10]
We compute the missing two- and three-loop NNLO matching coefficients in the 2HDM, and re-do the analysis to extract a lower bound on MH+ from the new experimental average (1.1)

Summary

Formalism

The formalism to compute the Wilson coefficients in the 2HDM can be taken over from the SM case [13, 14]. Since the additional degrees of freedom of the 2HDM are all heavy, they only influence the Wilson coefficients Ci of the operators Pi. In order to incorporate the 2HDM contribution in a manner that is analogous to the SM analysis of ref. The NNLO SM contributions to CiQ,SM(μ0) have been computed in refs. Constitutes the last missing element of the 2HDM Wilson coefficient evaluation that matters for B(B → Xsγ) at the NNLO. We reproduce the two-loop corrections CiH(2)(μ0) for i = 3, 4, 5, 6 that have been originally found in ref. In the following two subsections, we discuss our results for the Wilson coefficients in the SM and 2HDM. Several variables turn out to be of convenience in this context: y

Standard Model

Two Higgs Doublet Model

Ad Acu mt MH

Findings

Conclusions