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 $θ_{12}, θ_{23}, θ_{13}$ between three gauge fields $B_μ, W^3_{Lμ}, W^3_{Rμ}$, which produce mass eigenstates $A_{μ}, Z_{μ}, Z'_{μ}$, 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 $θ'$, which corresponds to the Weinberg angle $θ_{W}$ 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 $θ_{ij}$ can be expressed by $\varepsilon $ and $θ'$, 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 $θ'$ only, whereas heavy gauge bosons are described by two parameters $\varepsilon$ and $θ'$.