Michel parameter in 3-3-1 model with three lepton singlets

TL;DR

This paper analyzes the neutral gauge boson mass matrix in a 3-3-1 model with three lepton singlets, revealing eigenvalues, gauge boson mixings, and implications for the Michel parameter, highlighting the model's rich phenomenology.

Contribution

It provides an exact analysis of the gauge boson mass matrix and mixings in a 3-3-1 model with lepton singlets, including implications for the Michel parameter.

Findings

Exact eigenvalues of the neutral gauge boson mass matrix identified.

Mixings among W, Y, Z, Z', and X^0 gauge bosons analyzed.

Special conditions for the Michel parameter ρ derived.

Abstract

We show that the mass matrix of electrically neutral gauge bosons in the recently proposed model based on SU(3)_C X SU(3)_L X U(1)_X group with three lepton singlets [1] has two exact eigenvalues: a zero corresponding the photon mass and the second one equaling the mass of the imaginary component A_5\mu}. Hence the neutral non-Hermitian gauge boson X^0_\mu ( defined as \sqrt{2} X^0_\mu = A'_ 4\mu- i A_5\mu) is properly determined. With extra vacuum expectation value of the Higgs field n_2, there are mixings among the Standard Model W boson and the extra charged gauge boson Y carrying lepton number 2 (bilepton) as well as among neutral gauge bosons Z, Z' and X^0. These mixings lead to very rich phenomenology of the model. The leading order of the Michel parameter ($\rho$) has quite special form requiring an equality of the vacuum expectation values in the second step of spontaneous symmetry breaking, namely, k_1=k_2.