Electroweak phase transition in the economical 3-3-1 model

We consider the EWPT in the economical 3-3-1 (E331) model. Our analysis shows that the EWPT in the model is a sequence of two first-order phase transitions, $SU(3) \rightarrow SU(2)$ at the TeV scale and $SU(2) \rightarrow U(1)$ at the $100$ GeV scale. The EWPT $SU(3) \rightarrow SU(2)$ is triggered by the new bosons and the exotic quarks; its strength is about $1 - 13$ if the mass ranges of these new particles are $10^2 \,\mathrm{GeV} - 10^3 \,\mathrm{GeV}$. The EWPT $SU(2) \rightarrow U(1)$ is strengthened by only the new bosons; its strength is about $1 - 1.15$ if the mass parts of $H^0_1$, $H^\pm_2$ and $Y^\pm$ are in the ranges $10 \,\mathrm{GeV} - 10^2 \,\mathrm{GeV}$. The contributions of $H^0_1$ and $H^{\pm}_2$ to the strengths of both EWPTs may make them sufficiently strong to provide large deviations from thermal equilibrium and B violation necessary for baryogenesis.Comment: 17 pages, 9 figure

Directional Tykhonov well-posedness for optimization problems and variational inequalities

By using the so-called minimal time function, we propose and study a novel notion of directional Tykhonov well-posedness for optimization problems, which is an extension of the widely acknowledged notion of Tykhonov. In this way, we first provide some characterizations of this notion in terms of the diameter of level sets and admissible functions. Then, we investigate relationships between the level sets and admissible functions mentioned above. Finally, we apply the technology developed before to study directional Tykhonov well-posedness for variational inequalities. Several examples are presented as well to illustrate the applicability of our results.Comment: 2

Dilaton in Two-Time Physics as trigger of electroweak phase transition and inflation

Within the SP(2, R) symmetry, the Two-time model (2T model) has six dimension with two time dimensions. The model has a dilaton particle that makes the symmetry breaking differently from the Standard Model. By reducing the 2T metric to the Minkowski one (1T metric), we consider the electroweak phase transition picture in the 2T model with the dilaton as the trigger. Our analysis shows that Electro-weak Phase Transition (EWPT) is a first-order phase transition at the $200$ GeV scale, its strength is about $1 - 3.08$ and the mass of dilaton is in interval $[345, 625]$ GeV. Furthermore, the metric of 2T model can be reduced to the Randall-Sundrum model, so the dilaton acts as inflaton with the slow-roll approximation. Therefore the 2T-model indirectly suggests that extra-dimension can be also a source of EWPT and inflation. The EWPT problem can be used to determine scale parameters that refer to relationships between two metrics.Comment: 25 pages, 2 figure

Dynamics of Electroweak Phase Transition in the 3-3-1-1 Model

The bubble nucleation in the framework of 3-3-1-1 model is studied. Previous studies show that first order electroweak phase transition occurs in two periods. In this paper we evaluate the bubble nucleation temperature throughout the parameter space. Using the stringent condition for bubble nucleation formation we find that in the first period, symmetry breaking from $SU(3)\rightarrow SU(2)$, the bubble is formed at the nucleation temperature $T=150$ GeV and the lower bound of the scalar mass is 600 GeV. In the second period, symmetry breaking from $(SU(2)\rightarrow U(1)$, only subcritical bubbles are formed. This constraint eliminates the electroweak baryon genesis in the second period of the model