Maximum mass for the chiral σ-model fermion and implications for decoupling and ''classical'' heavy fermion decay

We find a limiting mass for the fermion in the σ-model, at the semi-classical level. This mass, Mmax, depends exclusively on the vacuum expectation value (VEV), <σ>, of the Higgs field. Below a critical value of the Yukawa coupling gc, the one-fermion ground state is realised, with the usual space uniform VEV of the Higgs, as a Yukawa fermion of mass, g<σ> < Mmax. For g > gc the one-fermion ground state has a space varying and 'topological' VEV with an energy MQ ≤ Mmax. For g much greater than gc the 'mass' of the topological fermion decreases with increasing g, going below zero at some g = g0 (g0 >> gc). At this point the theory is unstable both in the one-fermion (antifermion) and vacuum sectors. These features generalize to large Nc, where Nc is the degeneracy of fermion doublets. It is shown that the existence of the maximum mass of the fermion and the above behaviour with respect to the Yukawa coupling severely limit the conclusions on the decoupling of heavy fermions and the so-called unsuppressed or 'classical' decay of heavy fermions and technibaryons. (orig.)