Charges and Mass Spectrum in the Pisano-Pleitez-Frampton 3-3-1 Gauge Model

TL;DR

This paper applies an algebraic method to the Pisano-Pleitez-Frampton 3-3-1 gauge model, deriving exact mass spectra, couplings, and neutrino mass patterns, and exploring phenomenological implications including boson mass degeneracies.

Contribution

It demonstrates that the algebraic approach naturally reproduces Standard Model phenomenology and provides explicit formulas for masses and couplings in the 3-3-1 model.

Findings

Exact expressions for boson and fermion masses.

Couplings of charged and neutral currents derived.

Possible mass degeneracies between Z and Z' bosons.

Abstract

The Pisano-Pleitez-Frampton 3-3-1 model is revisited here within the framework of the general method for solving gauge models with high symmetries. This exact algebraical approach - proposed several years ago by one of us - was designed to include a minimal Higgs mechanism that spontaneously breaks the gauge symmetry up to the universal $U(1)_{em}$ electromagnetic one and, consequently, to supply the mass spectrum and the couplings of the currents for all the particles in the model. We prove in this paper that this powerful tool, when is applied to the PPF 3-3-1 model, naturally recovers the whole Standard Model phenomenology and, in addition, predicts - since a proper parametrization is employed - viable results such as: (i) the exact expressions for the boson and fermion masses, (ii) the couplings of the charged and neutral currents and (iii) a plausible neutrino mass pattern. A generalized Weinberg transformation is implemented, while the mixing between the neutral bosons $Z$ and $Z^{\prime}$ is performed as a necessary step by the method itself. Some phenomenological consequences are also sketched, including the strange possibility that simultaneously $m(Z)=m(Z^{\prime})$ and $m(W)=m(V)$ hold.