A minimal 3-3-1 model with naturally sub-eV neutrinos

TL;DR

This paper presents a minimal 3-3-1 model that naturally produces sub-eV neutrino masses using only three scalar triplets and a discrete symmetry, avoiding the need for a scalar sextet and suppressing proton decay.

Contribution

It introduces a minimal 3-3-1 model with an additional Z_3 symmetry that correctly generates all fermion masses and naturally light neutrinos without scalar sextets.

Findings

Successfully generates sub-eV neutrino masses.

Eliminates the need for scalar sextets in the model.

Suppresses proton decay via discrete symmetry.

Abstract

In the original version of the minimal SU(3)_C x SU(3)_L x U(1)_N model the masses of all quarks are correctly obtained by introducing three scalar triplets into the model, meanwhile the lepton mass generation requires the introduction of at least one scalar sextet. In this work we show that this scalar sextet is unable to yield the correct neutrino masses and mixing. In order to solve this puzzle in the most economical way, we evoke an additional Z_3 discrete symmetry, without including this sextet in the scalar spectrum, and propose a truly minimal 3-3-1 model capable of generating the correct masses and mixing of all fermions. Moreover, we show that our proposal leads to naturally light neutrinos with masses in the eV range, obtained with three scalar triplets only. Finally, the so called minimal 3-3-1 model is also in danger due to the presence of undesirable effective operators that lead to proton decay unless they are suppressed by extremely small couplings or, as we choose to employ in this work, are eliminated by some discrete symmetry.