One Loop Corrections To The Lightest Higgs Mass In The Minimal $\eta $ Model

We have evaluated the one loop correction to the bound on the lightest Higgs mass valid in the minimal, $E_{6}$ based, supersymmetric $\eta$ model. Under the assumption that the theory remains perturbative up to the $10^{16}$ GeV scale, we derive a conservative bound that decreases with the top mass for $M_t \leq 2 M_W$ and varies from $\sim 160$ GeV to $\sim 145$ GeV when $90 \leq M_t \leq 200$ GeV.