Renormalization-group-improved effective potential for the MSSM Higgs sector with explicit CP violation

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 LEP 2, the Tevatron and the LHC. In particular, CP violation could enable a relatively light Higgs boson to escape detection at LEP 2. energy CP-violating parameters of the MSSM that originate from experimental upper limits on the electron [23] and neutron [24] electric dipole moments (EDMs) [25,26,27,28,29,30,31,32,33,34,35]. Most of the EDM constraints affect the CP-violating couplings of the first two generations [25,26]. Thus, making the first two generations of squarks rather heavy, much above the TeV scale [27,28], is a possibility that can drastically reduce one-loop contributions to the neutron EDM, without suppressing the CP-violating phases of the theory. Another interesting possibility for avoiding any possible CP crisis in the MSSM is to arrange for cancellations among the different EDM terms, either at the level of short-distance diagrams [29] or (for the neutron EDM) at the level of the strong-interaction matrix elements for operators with s, u and d quark flavours [30,31]. Alternatively, one might require a specific form of non-universality in the soft trilinear Yukawa couplings [32,34].However, third-generation squarks can also give rise by themselves to observable effects on the electron and neutron EDMs through the three-gluon operator [33], through the effective coupling of the 'CP-odd' Higgs boson to the gauge bosons [34], and through two-loop gaugino/higgsino-mediated EDM graphs [35]. These different EDM contributions of the third generation can also have different signs and add destructively to the electron and neutron EDMs. In our phenomenological discussion, we take into account the relevant EDM constraints related to the CP-violating parameters of the stop and sbottom sectors. This paper is organized as follows: in Section 2 we calculate the co...

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