Radiatively Corrected Bound on the Light Higgs Mass in a Minimal Non Minimal Supersymmetric Standard Model

The neutral Higgs sector of the Minimal non Minimal Supersymmetric Standard Model is considered. By effective potential and R.G.E. supported method; an upper bound of the lightest Higgs is analysed. From the request of perturbativity of the coupling in the superpotential, adding the leading stop top contributions, the absolute bound of $\sim 130$ GeV for $90 GeV < m_t< 180 GeV$ and $M_{\tilde{t}} \simeq 1000 $ GeV is derived. The interesting dependence on $m_t$ for $\tan{\beta} \to 1$ is discussed