Spontaneous breaking of a global symmetry in the Minimum Supersymmetric $SU(3)_{C}\times SU(3)_{L}\times U(1)_{N}$ Model

TL;DR

This paper investigates the scalar potential of the supersymmetric 3-3-1 model, exploring symmetry breaking, the emergence of a Majoron, and mechanisms to remove it, with results consistent with experimental constraints.

Contribution

It introduces a study of symmetry breaking in the supersymmetric 3-3-1 model considering quantum number invariance and violation, providing insights into the scalar spectrum and Majoron removal.

Findings

Majoron appears when ${ m f F}$-invariance is maintained.

Allowing ${ m f F}$-violation removes the Majoron.

Mass spectrum aligns with experimental data.

Abstract

We present a preliminar study of the scalar potential of the usual scalars in the Minimal Supersymmetric $SU(3)_{C}\times SU(3)_{L}\times U(1)_{N}$ Model. We will consider the case in which all the usual neutral scalars fields of this model obtain vacuum expectation values. When we allow in our superpotential, only interactions that respect the invariance of the quantum number, ${\cal F}\equiv B+L$, where $B$ is the baryon number while $L$ is the total lepton number. We obtain, as in the minimal $SU(3)_{C}\times SU(3)_{L}\times U(1)_{N}$ model without supersymmetry, a Majoron. However, by allowing the violation of this quantum number, we can remove the Majoron in a mechanism similar to that recently presented in the Supersymmetric version of the scheme of Gelmini-Roncadelli. The mass spectrum obtained is in agreement with current experimental data.