Hierarchical radiative masses in a supersymmetric three-family model without Higgsinos

Abstract

We study the scalar potential and the mass spectrum of the supersymmetric extension of a three-family model based on the local gauge group $SU(3{)}_C\otimes SU(3{)}_L\otimes U(1{)}_X$, with anomalies canceled among the three families in a nontrivial fashion. In this model the slepton multiplets play the role of the Higgs scalars and no Higgsinos are needed, with the consequence that the sneutrino, the selectron and six other sleptons play the role of the Goldstone bosons of the theory. By introducing an Abelian anomaly-free discrete symmetry and aligning the vacuum in a convenient way, we get a consistent mass spectrum for the scalars and for the spin 1/2 quarks and charged leptons, where only the top and charm quarks and the tau lepton acquire tree level masses while the remaining ordinary charged fermions acquire radiative hierarchical masses.

Comments: RevTeX, 12 pages, 7 figures, 1 Table. v2: Clarifications added. Typos corrected. Two references added. v3: A mistake in the construction of the mass matrix for the charged scalars has been corrected. One appendix on the radiative mass of the exotic up quark has been added. One reference added. Main conclusions unchanged. v4: version accepted by Eur. Phys. J. C