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.Comment: 21 pages, 8 figure

CP Violation in the Higgs Sector and Phase Transition 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 first-order phase transition before the mixing reaches the maximal. 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 is light.Comment: 18 pages, 6 figures, LaTeX2

Scattering with Baryon Number Violation -- The Case of Higgs Particle Production --

\noindent A formalism based on path-integral expression of time-evolution operator during tunneling at a finite energy proposed by the authors is applied to $SU(2)$ gauge-Higgs system to produce Higgs particles with $\Delta B=1$. Instead of starting from instanton tunneling at the zero energy, a classical bounce solution giving sphaleron (instanton) action at high (low) energies is used as the tunneling configuration. Fourier transform of the bounce configuration in coherent state expression at the entrance and exit of the tunneling plays an important role. Numerical results at various energies for $M_H/M_W=1 \sim 2$ are given. Though the cross section with $\Delta B=1$ results from a severe cancellation of several large quantities in the leading order as occured in the instanton calculus, it seems unlikely that the cross section grows as largely as to reach unitarity bound at energies $E \leq E_{sph}$. It is pointed out that the actual value $g^2=0.418$ of the $SU(2)$ gauge coupling constant may be too large to take the weak coupling limit.}Comment: modified PHYZZX(included), 4 Figures (not included), SAGA-HE-46 : KYUSHU-HET-

Charge Generation in the Oscillating Background

The preheating after the inflation, which can be interpreted as particle creation in the oscillating inflaton background, provides a state far from thermal equilibrium. We extend the field theoretical treatment of the preheating by Linde et al. to the case of multicomponent complex scalars to show that some charges are created in this process, if C and CP are violated. A new possibility of baryogenesis based on this mechanism is also discussed.Comment: 18 pages, LaTeX 2e, 3 eps figure

Numerical Approach to CP-Violating Dirac Equation

We propose a new method to evaluate the chiral charge flux, which is converted into baryon number in the framework of the charge transport scenario of electroweak baryogenesis. By the new method, one can calculate the flux in the background of any type of bubble wall with any desired accuracy.Comment: 14 pages, epsf.sty is needed, 3 figures appende

CP Violating Bubble Wall and Electroweak Baryogenesis

The electroweak baryogenesis depends on the profile of the CP-violating bubble wall created at the first order phase transition. We attempt to determine it by solving the coupled equations of motion for the moduli and phases of the two Higgs doublets at the transition temperature. A variety of CP-violating bubble walls are classified by boundary conditions. We point out that a sufficiently small explicit CP violation gives nonperturbative effects to yield the baryon asymmetry of the universe.Comment: 19 pages, 6 EPS figures, uses epsf.st

Spontaneous CP Violation at Finite Temperature in the MSSM

By studying the effective potential of the MSSM at finite temperature, we find that CP can be spontaneously broken in the intermediate region between the symmetric and broken phases separated by the bubble wall created at the phase transition. This type of CP violation is necessary to have a bubble wall profile connecting CP conserving vacua, while violating CP halfway and generating sufficient baryon number without contradiction to the experimantal bounds on CP violations. Several conditions on the parameters in the MSSM are found for CP to be broken in this manner.Comment: 26 pages, LaTeX, 16 eps figures (epsf.sty is needed

Chiral Charge Flux and Electroweak Baryogenesis

By treating CP-violating interaction of the electroweak bubble wall as a perturbative term, chiral charge flux through the bubble wall is estimated. It is found that the absolute value of the flux $F_Q$ has a sharp peak at $m_0 \sim a \sim T$ with $F_Q/(u T^3) \sim 10^{-3}\, (Q_L-Q_R)\,\Delta \theta$. Here $m_0$ is the fermion mass, $1/a$ is the wall thickness, $T$ is the temperature at which the bubbles are growing, $u$ is the wall velocity, $Q_{L(R)}$ is the chiral charge of the relevant left(right)-handed fermion and $\Delta\theta$ is the measure of CP violation.Comment: 10 pages, 4 figures ( not included, hard copies are available upon request ), plain TeX with phyzzx

The relative-age effect in male Japanese football: a cross sectional analysis from youth to senior competitive level

The objective of this study was to examine the magnitude and persistence of the Relative-Age Effect (RAE) in competitive Japanese youth and senior football. A cross-sectional analysis of birthdate distributions of Japanese male youth academy football players (n= 4,488) from the U12 (n=268), U13 (n=481), U14 (n=464), U15 (n=483), U18 (n=1059) and professional players (n=1733) in the 2022 season was conducted. Chi-square goodness of fit tests and Cramer’s V tests were carried out to reveal the incidence and effect size of the RAE across the age categories. A significant RAE (P< .001) was found. It became more pronounced with age, peaking in the U18 age group (Cramer's V= 0.436; Q1/Q4 OR 6.04) before declining in senior professional players (Cramer's V= 0.204; Q1/Q4 OR=2.23). The organisation of youth competition in Japan, with a transition from annual age groups up to U15 to the U18 age group representing three years (U16, U17, and U18) appears to increase the selection bias towards early born players to the detriment of those born later in the age group. However, the transition to senior football saw, compared with the U18 proportions, a reduced proportion of Q1 players, a very similar proportion of Q2players and increased proportions of Q3 and particularly Q4. The clear implication is that a Q3 and Q4 youth player represents a better prospect for senior professional football than Q1 or Q2 and Q2 than Q1

Dependence of the BEC transition temperature on interaction strength: a perturbative analysis

We compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93 a\rho^{1/3}$, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and $\rho$ is the particle number density.Comment: 14 pages (RevTeX