Higgs revised in supersymmetric economical 3-3-1 model with $$B/\mu $$-type terms

We re-investigate the scalar potential and the Higgs sector of the supersymmetric economical 3-3-1 model (SUSYE331) in the presence of the \(B/\mu \)-type terms, which has many important consequences. First, the model contains no massless Higgs fields. Second, we prove that the soft mass parameters of the Higgses must be at the \(\hbox {SU}(3)_L\) scale. As a result, the masses of the Higgses drift toward this scale except one light real neutral Higgs with the mass of \(m_Z|c_{2\gamma }|\) at the tree level. We also show that there are some Higgses containing many properties of the Higgses in the minimal supersymmetric standard model (MSSM), especially in the neutral Higgs sector. One exact relation in the MSSM, \(m^2_{H^{\pm }}=m^2_{A}+m^2_W\), is still true in the SUSYE331. Based on this result we make some comments on the lepton flavor violating decays of these Higgses as one of signatures of new physics in the SUSYE331 model which may be detected by present colliders.