Koichi Funakubo

The higgs sector in the next-to-MSSM

We study the Higgs sector in the next-to-minimal supersymmetric standard model both with and without explicit CP violation, focusing on the case of a weak-scale expectation value of the singlet field. We scan a wide range of the parameter space to determine allowed regions by requiring that the electroweak vacuum be the global minimum of the effective potential and that the neutral Higgs bosons with moderate gauge coupling be heavier than the lower bound on the Higgs boson in the standard model. Among the allowed sets of parameter values, some sets yield the situation in which the light Higgs bosons couple with the Z boson too weakly for observation to be possible in present collider experiments. For such parameter sets, we determine an upper bound on the charged Higgs mass that is attainable in LHC.

Electroweak phase transition, critical bubbles and sphaleron decoupling condition in the MSSM

The electroweak phase transition and the sphaleron decoupling condition in the minimal supersymmetric standard model are revisited taking the latest experimental data into account. The light Higgs boson scenario and the ordinary decoupling limit, which are classified by the relative size between the CP-odd Higgs boson mass and Z boson mass, are considered within the context of electroweak baryogenesis. We investigate v/T at not only the critical temperature at which the effective potential has two degenerate minima but also the nucleation temperature of the critical bubbles, where v is a vacuum expectation value of the Higgs boson and T denotes a temperature. It is found that v/T at the nucleation temperature can be enhanced by about 10% compared to that at the critical temperature. We also evaluate the sphaleron decoupling condition including the zero mode factors of the fluctuations around sphaleron. It is observed that the sphaleron decoupling condition at the nucleation temperature is given by v/T > or approx. 1.38 for the typical parameter sets. In any phenomenologically allowed region, v/T at both the critical and nucleation temperatures cannot be large enough to satisfy such a sphaleron decoupling condition.

The Effective Potential of Electroweak Theory with Two Massless Higgs Doublets at Finite Temperature

The effective potential of electroweak theory with two massless Higgs doublets at finite temperature is studied. We investigate phase structure and critical temperature in this model by numerical analysis without high-temperature expansion. The phase transition is found to be of first order. The critical temperature is shown to be relatively low for typical scalar masses. The free energy of the critical bubble is calculated with some approximations and we find that the bubble nucleation can occur at a temperature a little below the critical temperature. We also discuss the possibility of the electroweak baryogenesis

Phase Transitions in the NMSSM

We study phase transitions in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with the weak scale vacuum expectation values of the singlet scalar, constrained by Higgs spectrum and vacuum stability. We find four different types of phase transitions, three of which have two-stage nature. In particular, one of the two-stage transitions admits strongly first order electroweak phase transition, even with heavy squarks. We introduce a tree-level explicit CP violation in the Higgs sector, which does not affect the neutron electric dipole moment. In contrast to the MSSM with the CP violation in the squark sector, a strongly first order phase transition is not so weakened by this CP violation.

CP violation and baryogenesis at the electroweak phase transition

We report a recent attempt to relate

CP Violation in the Higgs Sector and a Phase Transition in the MSSM

CP

Transitional CP Violation in the MSSM and Electroweak Baryogenesis

violation in the electroweak theory with two Higgs doublets to the baryon asymmetry generated at the electroweak phase transition, after surveying the scenario of the electroweak baryogenesis.

Spontaneous CP violation at finite temperature in the MSSM

We investigate the electroweak phase transition in the presence of a large CP violation in the squark sector of the MSSM. When the CP violation is large, scalar-pseudoscalar mixing of the Higgs bosons occurs, and a large CP violation in the Higgs sector is induced. It, however, weakens the first-order phase transition before the mixing reaches its maximal level. Even when the CP violation in the squark sector is not so large that the phase transition is strongly first order, the phase difference between the broken and symmetric phase regions grows to O(1), which leads to successful baryogenesis when the charged Higgs bosons are light.

Fermion scattering off a CP-violating electroweak bubble wall.

Electroweak baryogenesis depends on the profile of the bubble wall created in the first-order phase transition. It is pointed out that CP violation in the Higgs sector of the MSSM could become large enough to explain the baryon asymmetry. We confirm this by solving the equations of motion for the Higgs fields with the effective potential at the transition temperature. That is, we present an example such that the transitional CP violation is realized and show the possibility that the baryon asymmetry of the universe may be produced, if marginally, by the

Sphalerons in the NMSSM

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