Renormalization-Group-Improved Effective Potential for the MSSM Higgs Sector with Explicit CP Violation

TL;DR

The paper develops a comprehensive RG-improved one-loop effective potential for the MSSM Higgs sector with explicit radiative CP violation from soft trilinear couplings to third-generation squarks. It computes charged and neutral Higgs mass matrices incorporating two-loop leading-log corrections and one-loop threshold effects, along with threshold-resummed top and bottom Yukawa couplings, yielding precise predictions for Higgs masses and couplings. The study demonstrates that CP violation can substantially modify Higgs-boson production and decay patterns, potentially allowing a light Higgs to escape detection at LEP2 while heavy Higgs states exhibit pronounced CP-violating mixing, with implications for Tevatron and LHC searches. It also discusses decoupling behavior in the light-Higgs sector and non-decoupling effects in the heavier sector, EDM constraints, and the relevance for electroweak baryogenesis, providing a self-consistent framework and accompanying code for practical predictions.

Abstract

We perform a systematic study of the one-loop renormalization-group-improved effective potential of the minimal supersymmetric extension of the Standard Model (MSSM), including CP violation induced radiatively by soft trilinear interactions related to squarks of the third generation. We calculate the charged and neutral Higgs-boson masses and couplings, including the two-loop logarithmic corrections that arise from QCD effects, as well as those associated with the top- and bottom-quark Yukawa couplings. We also include the potentially large two-loop non-logarithmic corrections induced by one-loop threshold effects on the top- and bottom-quark Yukawa couplings, due to the decoupling of the third-generation squarks. Within this minimal CP-violating framework, the charged and neutral Higgs sectors become intimately related to one another and therefore require a unified treatment. In the limit of a large charged Higgs-boson mass, M_{H^+} >> M_Z, the lightest neutral Higgs boson resembles that in the Standard Model (SM), and CP violation occurs only in the heavy Higgs sector. Our analysis shows that sizeable radiative effects of CP violation in the Higgs sector of the MSSM may lead to significant modifications of previous studies for Higgs-boson searches at LEP2, the Tevatron and the LHC. In particular, CP violation could enable a relatively light Higgs boson to escape detection at LEP2.

Figures (9)

• Figure 1: Numerical estimates of (a) $M_{H_1}$ and $M_{H_2}$ and (b) $g^2_{H_iZZ}$ as functions of ${\rm arg}\, (A_t)$, for the indicated choices of MSSM parameters. Solid lines correspond to ${\rm arg}\, (m_{\tilde{g}}) = 0$, dashed lines to ${\rm arg}\, (m_{\tilde{g}}) = 90^\circ$.
• Figure 2: As Fig. \ref{['fig:cph1']}, but with $\mu = 4$ TeV, $|A_t| = |A_b| = 2$ TeV and $M_{\rm SUSY} = 1$ TeV.
• Figure 3: As in Fig. \ref{['fig:cph1']}, but with $\tan\beta = 20$.
• Figure 4: As in Fig. \ref{['fig:cph3']}, but with $M_{H^+} = 135$ GeV.
• Figure 5: Numerical estimates of (a) $M_{H_1}$ and (b) $2|M_{H_2}-M_{H_3}|/(M_{H_2} + M_{H_3})$ as functions of the CP-violating phase arg($A_t$). Lower values of the same line type correspond to ${\rm arg}\, (m_{\tilde{g}}) = 0$, the higher ones to ${\rm arg}\, (m_{\tilde{g}}) = 90^\circ$.