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 $B_{\mu },W_{L\mu }^3,W_{R\mu }^3$, which produce mass eigenstates $A_{\mu },Z_{\mu },Z_{\mu }^{\mathrm{\prime }}$, when $G = SU(2)L\times SU(2)R\times U(1){B-L} \times D$isspontaneouslybrokendownuntil$U(1){em}$. We find a new mixing angle ${\theta }^{\mathrm{\prime }}$, which corresponds to the Weinberg angle $\theta {W}$inthestandardmodelwiththe$SU(2){L}\times U(1)_{Y}$ gauge symmetry, from these mixing angles. It is then shown that any mixing angle ${\theta }_{ij}$ can be expressed by $\epsilon$ and ${\theta }^{\mathrm{\prime }}$, 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 ${\theta }^{\mathrm{\prime }}$ only, whereas heavy gauge bosons are described by two parameters $\epsilon$ and ${\theta }^{\mathrm{\prime }}$.