New Mixing Angles in the Left-Right Symmetric Model

TL;DR

This paper introduces a new mixing angle in the left-right symmetric model that relates to the Weinberg angle, providing a unified way to express gauge boson mixings based on gauge coupling ratios.

Contribution

The paper identifies a new mixing angle in the left-right symmetric model and expresses all gauge mixing angles in terms of this angle and the gauge coupling ratio, offering a novel parametrization.

Findings

A new mixing angle $ heta '$$ is identified, corresponding to the Weinberg angle.

Light gauge bosons are described solely by $ heta '$.

Heavy gauge bosons depend on both $ heta '$ and the coupling ratio $oldsymbol{ ext{varepsilon}}$.

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 $B_\mu , W^3_{L\mu }, W^3_{R\mu }$, 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 $\theta '$.