The economical SU(3)_C X SU(3)_L X U(1)_X model

TL;DR

This paper details the structure, gauge boson mixing, and scalar sector of a minimal 3-3-1 gauge model, exploring lepton-number violation, gauge boson mass splitting, and fermion mass generation.

Contribution

It provides a comprehensive analysis of the minimal scalar sector and gauge boson mixing in the 3-3-1 model, including exact diagonalization and phenomenological constraints.

Findings

Lepton-number violation arises from the vacuum expectation value u.

Gauge boson mixing leads to distinct mass eigenstates for W, Z, Z', and bileptons.

The model predicts specific scalar and gauge boson masses consistent with experimental constraints.

Abstract

In this report the SU(3)_C X SU(3)_L X U(1)_X gauge model with minimal scalar sector, two Higgs triplets, is presented in detail. One of the vacuum expectation values $u$ is a source of lepton-number violations and a reason for mixing among charged gauge bosons--the standard model W^\pm and the bilepton gauge bosons Y^\pm as well as among the neutral non-Hermitian bilepton X^0 and neutral gauge bosons--the Z and the new Z'. An exact diagonalization of the neutral gauge boson sector is derived and bilepton mass splitting is also given. Because of these mixings, the lepton-number violating interactions exist in both charged and neutral gauge boson sectors. Constraints on vacuum expectation values of the model are estimated and u \simeq O(1) GeV, v \simeq v_weak = 246 GeV, and \omega \simeq O(1) TeV. In this model there are three physical scalars, two neutral and one charged, and eight Goldstone bosons--the needed number for massive gauge bosons. The minimal scalar sector can provide all fermions including quarks and neutrinos consistent masses in which some of them require one-loop radiative corrections.