Renormalization-group-improved unitarity bounds on the Higgs-boson and top-quark masses

A renormalization-group-improved perturbative unitarity bound for elastic scattering amplitudes is proposed. This prescription leads to upper bounds on the Higgs-boson and top-quark masses as a function of the energy at which perturbative unitarity is violated and new physics enters. Upper bounds on the scale of new physics in models with no Higgs boson are also discussed.