Upper Bounds on the Lightest Higgs Boson Mass in General Supersymmetric Standard Models

In a general supersymmetric standard model there is an upper bound $m_h$ on the tree level mass of the $CP=+1$ lightest Higgs boson which depends on the electroweak scale, $\tan \beta$ and the gauge and Yukawa couplings of the theory. When radiative corrections are included, the allowed region in the $(m_h,m_t)$ plane depends on the scale $\Lambda$, below which the theory remains perturbative, and the supersymmetry breaking scale $\Lambda_s$, that we fix to $1\ TeV$. In the minimal model with $\Lambda=10^{16}\ GeV$: $m_h<130\ GeV$ and $m_t<185\ GeV$. In non-minimal models with an arbitrary number of gauge singlets and $\Lambda=10^{16}\ GeV$: $m_h<145\ GeV$ and $m_t<185\ GeV$. We also consider supersymmetric standard models with arbitrary Higgs sectors. For models whose couplings saturate the scale $\Lambda=10^{16}\ GeV$ we find $m_h<155\ GeV$ and $m_t<190\ GeV$. As one pushes the saturation scale $\Lambda$ down to $\Lambda_s$, the bounds on $m_h$ and $m_t$ increase. For instance, in models with $\Lambda=10\ TeV$, the upper bounds for $m_h$ and $m_t$ go to $415\ GeV$ and $385\ GeV$, respectively.