Is there an upper limit to fermion masses?

Abstract

A fermion mass generated by spontaneous symmetry breaking is proportional to its Yukawa coupling $y$ to a Higgs field. Like the Higgs-field self-copuling, $y$ may well be trivial and diverge at a finite energy scale ${\ensuremath{\Lambda}}_{f}$, corresponding to an upper limit on fermion masses. We verify this by solving a simple model by means of a $\frac{1}{N}$ expansion. Applied to the standard model, this suggests that there is an upper limit to quark and lepton masses. These results have implications for the "decoupling" of heavy fermions and bear on the issue of whether apparently "anomalous" gauge theories can be consistently quantized.