New Mixing Angles in the Left-Right Symmetric Model

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 $B_\mu , W^3_{L\mu }, W^3_{R\mu }$, which produce mass eigenstates $A_{\mu }, Z_{\mu }, Z'_{\mu }$, 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 $\theta '$, 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 $\varepsilon$ and $\theta '$, where $\varepsilon = g_L/g_R$ is a ratio of running left-right gauge coupling strengths. We observe that light gauge bosons are described by $\theta'$ only, whereas heavy gauge bosons are described by two parameters $\varepsilon$ and $\theta '$.