New Mixing Angles in the Left-Right Symmetric Model

Abstract

In the left-right symmetric model neutral gauge fields are characterized by three mixing angles ${\theta }_{12},{\theta }_{23},{\theta }_{13}$ between three gauge fields $B_{\mu },W_{L\mu }^3,W_{R\mu }^3$, which produce mass eigenstates $A_{\mu },Z_{\mu },Z_{\mu }^{\prime }$, when $G=SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L}\times D$ is spontaneously broken down until $U(1{)}_{em}$. We find a new mixing angle ${\theta }^{\prime }$, which corresponds to the Weinberg angle ${\theta }_W$ in the standard model with the $SU(2{)}_L\times U(1{)}_Y$ gauge symmetry, from these mixing angles. It is then shown that any mixing angle ${\theta }_{ij}$ can be expressed by $\epsilon$ and ${\theta }^{\prime }$, where $\epsilon =g_L/g_R$ is a ratio of running left-right gauge coupling strengths. We observe that light gauge bosons are described by ${\theta }^{\prime }$ only, whereas heavy gauge bosons are described by two parameters $\epsilon$ and ${\theta }^{\prime }$.

Comments: 15 pages, No figures