The Phenomenology of Sphaleron in Modified Mirror Model

Abstract

We investigate sphaleron solutions of the field equations in the modified mirror model. This model is based on SU(3)$_1$ $\otimes$ SU(3)$_2$ $\otimes$ SU(2)$_L$ $\otimes$ SU(2)$_R$ $\otimes$ U(1)$_{Y}$ $\otimes$ U(1)$_{X}$ gauge group. Different from the usual Weinberg-Salam theory, we will have two types of fields, the ordinary (standard model) and its mirror partners. In this paper, we will focus only on the case when the doublet scalar of the mirror sector has a very large vacuum expectation value (VEV) compared to the VEV of the SM Higgs. We study two scenarios related to the sphaleron solutions in this model, depending on the value of the coupling $\alpha$. For the case of $\alpha=0$, each sector has its sphaleron and the sphaleron energy depends on the VEV of scalars for each sector. In the case $\alpha \neq 0$, we find that the sphaleron energy in the SM sector can be either increased or decreased depending on the relative sign of the coupling $\alpha$.