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 $\theta '$.
Categories: hep-ph