Lepton flavour violating decays of $\mu$ and $\tau$ lepton in a gauge group $S{U}_L(2)\times S{U}_R(2)\times S{U}_l(2)$

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 $Y_1=-L=\pm 1$ 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 ${\left(\frac{{\sin }^2{\theta }_W}{1-2{\sin }^2{\theta }_W}\right)}^2{\left(\frac{m_{W_L}}{m_Y}\right)}^4$.

Comments: 10 pages, no figure