Lepton flavour violating decays of $\mu$ and $\tau$ lepton in a gauge group $SU_L(2)\times SU_R(2)\times SU_l(2)$

TL;DR

This paper proposes a gauge group extension for charged lepton flavor violation involving a new $SU(2)_Y$ symmetry, analyzing its symmetry breaking and implications for $$ and $ au$ decays.

Contribution

It introduces a novel gauge group structure with spontaneous symmetry breaking to explain lepton flavor violating decays and derives the associated decay probabilities.

Findings

Decay probability depends on the mixing angle and mass ratio of gauge bosons.

The model recovers features of left-right electroweak unification.

Predicted decay rates provide testable signatures for new physics.

Abstract

The electroweak unification group $ SU(2)_L\times SU(2)_R\times SU(2)_Y $ is proposed for the charged lepton flavor violating decays of the muon ($\mu$) and tau ($\tau$) leptons. The group $SU(2)_Y$ is in the lepton space. The left-handed leptons and anti-leptons are assigned to the fundamental representation $(2,2,\bar{2})$ of the semi-simple group. The gauge group $SU(2)_Y$ is spontaneously broken to $U(1)_{Y_1}$, where $Y_1=-L=\pm1$ is the hypercharge, by introducing a scalar multiplet $\Sigma$ which belongs to the triplet representation 3 of the $SU(2)_Y$ and is singlet under $SU(2)_L\times SU(2)_R$. At this stage charged vector bosons $Y^\pm$ of $SU(2)_Y$ which mediate the lepton flavor violating decays acquire masses and are decoupled with one Higgs scalar $H_\Sigma^0$. The residual group $SU(2)_L\times SU(2)_R\times U(1)_{Y_1}$ has all the features of the left-right electroweak unification group extensively studied in the literature. The probability for lepton flavor violating decays is $\left(\frac{\sin^2\theta_W}{1-2\sin^2\theta_W}\right)^2\left(\frac{m_{W_L}}{m_Y}\right)^4$.