Yukawa-coupling-generated fermion masses on the lattice

Yukawa couplings are studied on the lattice for fermions coupled to scalar fields of a single component λφ4 theory. Quenched calculations of the physical fermion mass MF are carried out in the broken phase at zero bare fermion mass and for Yukawa couplings ranging between 1 and 2.5. Our results, when combined with recent nonperturbative determinations of the scalar field wave function renormalization Z by Huang, Manousakis and Polonyi, indicate that the ratio MF/<φren> vanishes as one approaches the critical point. This lends support to the idea that Yukawa coupling-generated fermion masses cannot become arbitrarily large without, at the same time, the model ceasing to be a valid effective low-energy theory. (orig.)