Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters

TL;DR

This paper computes comprehensive two-loop QCD corrections to the lightest Higgs-boson mass in the MSSM with complex parameters, enhancing prediction accuracy for collider tests and including the effects of complex phases.

Contribution

It provides the first complete two-loop QCD correction calculation for the MSSM Higgs mass with complex parameters, incorporating full momentum and mass dependence.

Findings

Significant impact of complex phases on Higgs mass predictions.

Enhanced precision in MSSM Higgs mass calculations.

Results integrated into the FeynHiggs code for public use.

Abstract

Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can be inferred. For an improved theory accuracy, we compute all two-loop corrections involving the strong coupling for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling and Yukawa couplings, leading to terms of $\mathcal{O}{\left(\alpha\alpha_s\right)}$ and $\mathcal{O}{\left(\sqrt{\alpha_{q_1}}\sqrt{\alpha_{q_2}}\alpha_s\right)}$, ($q_{1,2}=t,b,c,s,u,d$). The full dependence on the external momentum and all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach which is flexible in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code $\texttt{FeynHiggs}$ is adopted. For the evaluation of the results, a total of $513$ two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program $\texttt{SecDec}$. A comparison with existing results in the limit of real parameters and/or vanishing external momentum is carried out, and the impact on the lightest Higgs-boson mass is discussed, including the dependence on complex phases. The new results will be included in the public code $\texttt{FeynHiggs}$.