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.Comment: 21 pages, 8 figure

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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. §1. IntroductionThe search for the Higgs boson is one of the most important issue of high-energy particle physics, because the Higgs boson is the only unobserved particle in the minimal standard model (MSM). The results of the LEP 2 experiment place a limit on the MSM-Higgs mass: m h > 114.4 GeV with 95% CL. 1), 2) Although there are some theoretical restrictions on the Higgs mass, it cannot be predicted in the MSM framework, because the Higgs self-coupling is a free parameter. Supersymmetric extensions of the MSM, which were formulated with the goal of solving the hierarchy problem, place limitations on the possible range of the Higgs mass, because of the selfcoupling resulting from the gauge couplings. Among such extensions, the minimal supersymmetric Standard Model (MSSM) has been extensively studied and is known to give an upper bound on the mass of the lightest Higgs boson, namely, m h ≤ m Z at the tree level. This bound seems somewhat severe, but it is modified by radiative corrections, through which it becomes m h ≤ 135 GeV at the two-loop level. These corrections come mainly from the loops of the top quark and squark. 3)The MSSM contains a µ-parameter in the superpotential. It enters the Higgs potential with the soft scalar masses to determine the vacuum expectation value (VEV) of the Higgs fields. Thus, µ must take a value on the order of the weak scale, which is much smaller than the GUT scale or Planck scale. However, there is no a priori reason for µ to have such a small value. One solution of this so-called µ-problem is to substitute a VEV of an extra gauge-singlet field for the parameter µ. The NMSSM is among the models that have a gauge-singlet Higgs

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. §1. IntroductionThe baryon asymmetry of the universe (BAU) is one of the most obvious facts regarding the makeup of the universe, and its explanation has been a longstanding problem in astrophysics. 1) To explain the light-element abundances within the framework of the standard big-bang nucleosynthesis, it is required that 2) It is well known that in order to obtain this asymmetry starting from a baryonsymmetric state, three requirements must be satisfied: baryon number violation, C and CP violation, and departure from equilibrium. 3) In general, electroweak theories satisfy baryon number violation through the chiral anomaly and may be capable of describing the BAU. 4) In the minimal standard model (MSM), the main source of CP violation comes from the phase δ KM in the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix. Although this phase is able to account for the experimentally observed CP violation in neutral K-mesons and, as recently measured, in the B d system, it has been shown that it is not possible to generate sufficient BAU through δ KM . Furthermore, the strength of the phase transition is so weak in the MSM in the case that the Higgs scalar is heavier than 115 GeV 5), 6) that the universe is approximately in equilibrium when the process of baryon number change is in effective.In the context of the supersymmetric (SUSY) extension of the MSM, it has been * ) E-mail: funakubo@cc.saga-u.ac.jp * * ) E-mail: tao@higgs.phys.kyushu-u.ac.jp * * * ) E-mail: ftoyoda@fuk.kindai.ac.jp Funakubo, S. Tao and F. Toyoda pointed out that in the presence of a light stop, the electroweak phase transition (EWPT) can be strong enough for baryogenesis to take place. 7) Moreover, SUSY models contain many complex parameters as new CP -violating sources in addition to δ KM : the Higgs bilinear term, µ, and soft SUSY breaking terms (gaugino masses and scalar trilinear couplings). 8) In addition to these complex parameters, a non zero relative phase of the expectation values of the two Higgs doublets θ might be induced by radiative and finite-temperature effects, although it vanishes at the tree level. Without any complex parameter, a phase θ could be induced by loop effects of SUSY particles. This idea of spontaneous CP violation was studied at zero temperature in the minimal supersymmetric standard model (MSSM), and it was pointed out that there inevitably appears a pseudoscalar boson as li...

We study sphaleron solutions in the next-to-minimal supersymmetric standard model. We find that the boundary condition on the singlet field at the origin of the radial coordinate is of Neumann type, while the other boundary conditions are of Dirichlet type. The sphaleron energy takes almost the same value as in the MSSM for wide range of parameters, in spite of the negative contribution from the cubic term in the Higgs potential.Comment: 15 pages, 4 figure