The $\mu\nu$SSM with an extra U(1)

TL;DR

This paper extends the $ u$SSM by adding an extra U(1) gauge symmetry, addressing issues like proton decay, neutrino masses, and Higgs mass bounds, while ensuring anomaly cancellation and viable electroweak symmetry breaking.

Contribution

It introduces a new U(1) extension of the $ u$SSM with anomaly cancellation, viable charge assignments, and consistent phenomenology including neutrino masses and Higgs mass predictions.

Findings

Six viable U(1) charge assignments identified with extra matter.

Electroweak symmetry breaking is consistent with experimental constraints.

The lightest Higgs mass can reach approximately 120 GeV.

Abstract

The $\mu\nu$SSM solves the $\mu$ problem of the MSSM and generates correct neutrino masses by simply using right-handed neutrinos. This mechanism implies that only dimensionless trilinear terms, breaking R-parity, are present in the superpotential. We present an extension of the $\mu\nu$SSM with an extra U(1) gauge symmetry. We use the extra U(1) charges of the matter fields to forbid the presence in the superpotential of renormalizable and non-renormalizable baryon number violating operators, the trilinear operator producing a domain wall problem, and bilinear operators such as the $\mu$ term and the Majorana masses. We apply the anomaly cancellation conditions associated to the extra U(1), to constrain the values of the U(1) charges. We find that six assignments of the U(1) charges to the matter fields are viable, once extra matter is introduced. In particular, three generations of vector-like color triplets and $SU(2)_L$ doublets, as well as six Standard Model singlets are necessary. Electroweak symmetry breaking is viable in the model, with wide regions of the parameter space fulfilling the experimental constraints on the existence of a new gauge boson $Z'$. Neutrinos and the extra gaugino mix with the MSSM neutralinos, producing a generalized see-saw matrix that can reproduce the experimental results on neutrino masses. Finally, we have estimated the tree-level upper bound on the lightest Higgs mass, finding that it can be as large as about 120 GeV.