A Cutoff Constrained by the Oblique Parameters in Electroweak Theory with Two Massless Higgs Doublets

Electroweak theory with two massless Higgs doublets is studied by solving renormalization group equations for coupling constants in one-loop approximation. A cutoff~$\Lambda$, at which one of quartic couplings in the Higgs potential blows up, is obtained by imposing constraints from the oblique parameter $T$ on the quartic couplings at low energy. We find $\Lambda \simeq 0.52\sim 8.4$~TeV at the Higgs mass $M_H=100$ GeV. The cutoff $\Lambda$ is at most about $60$ TeV even if we take into account the LEP lower bound of $M_H\simeq 64$ GeV. It cannot reach the Planck or GUT scale due to severe experimental constraints. It is impossible in the model to realize a large gauge hierarchy as suggested many years ago by S. Weinberg.