Vacuum Instability and New Constraints on Fermion Masses

I show that, in the Weinberg-Salam model with one Higgs doublet, in order for the physical vacuum to be an absolute minimum (in the one-loop approximation), certain requirements on the fermion masses have to be met. Specifically, the quantity ${\left\{\Sigma i^{}{m_{f_i}}^4\right\}}^{\frac{1}{4}}$, where the summation extends over fermions, is bounded from above by approximately 133.5 GeV $({{sin}^2\theta }_{\mathrm{W}}=0.25) or 137.7$ GeV (${{sin}^2\theta }_{\mathrm{W}}=0.2\mathrm{}$).