Probing the Desert with Fermion Masses

We use the SU(3) ⊗ SU(2) ⊗ U(1) renormalization-group equations to place upper limits on the scale where new physics beyond the standard model must emerge. Our bounds rely solely on the structure of the renormalization-group equations and on the magnitudes of heavy-quark masses. For example, if $\Sigma m_q^2>~{\left(450\mathrm{} \mathrm{GeV}\right)}^2$, new physics must be found below ${10}^5$ GeV.