Scalar sector of Supersymmetric ${SU}(3)_C\otimes {SU}(3)_L \otimes {U}(1)_N$ Model with right-handed neutrinos

Abstract

We investigate a scalar sector of the supersymmetric $ SU_C(3) \otimes SU_L(3)\otimes U_N(1)$ model with right-handed neutrinos. The mass spectra are derived. We show that only neutral Higgs sector with lepton number L=0 could have a VEV. There is no mixing between scalars having L=0 and bilepton scalars having L=2. There are six Goldstone bosons: two in neutral sector, three in pseudo-scalar sector and one in charged scalar sector. For a given set of input parameters (five from the $F$ terms and two from the soft term) all the scalar sectors in this model contain the upper limit of 230 GeV to the mass of the lightest scalar, which are in agreement with the lower limit of the SM Higgs boson obtained by LEP.