A different approach to electroweak interactions without using any $SU(2)_L$ doublet

Abstract

We know that demanding $SU(2)_L\times U(1)_Y$ gauge symmetry of Lagrangian is a "sufficient" condition to describe electroweak interactions, however, in this paper, we have tried to find whether it's a "necessary" condition or not. We have used a different approach to describe electroweak interactions without using any $SU(2)_L$ doublet or $SU(2)_L$ generator and incorporate some new physics aspects into theory. In this method, we only need local gauge invariance of Lagrangian under a "generalised $U(1)_Q$ gauge transformation", where $Q$ is electric charge (not to be confused with usual $U(1)$ transformation). Under this gauge transformation, all charged fields including charged gauge bosons transform as $H_{(\mu)}\rightarrow H_{(\mu)}e^{iq_h\theta}$ and all neutral gauge bosons transforms as $V_\mu\rightarrow V_\mu+\Lambda \partial_\mu \theta$. Nevertheless, $SU(2)_L$ symmetry can be restored by imposing constraints on some parameters and thus standard model can be considered as a special case of this model. Hence, it turns out that $SU(2)_L\times U(1)_Y$ gauge symmetry is a "sufficient" but "not necessary" condition for electroweak interactions.