  In this contribution we lay down a lattice setup that allows for the
non-perturbative study of a field theoretical model where a SU(2) fermion
doublet, subjected to non-Abelian gauge interactions, is also coupled to a
complex scalar field doublet via a Yukawa and an "irrelevant" Wilson-like term.
Using naive fermions in quenched approximation and based on the renormalized
Ward identities induced by purely fermionic chiral transformations, lattice
observables are discussed that enable: a) in the Wigner phase, the
determinations of the critical Yukawa coupling value where the purely fermionic
chiral transformation become a symmetry up to lattice artifacts; b) in the
Nambu-Goldstone phase of the resulting critical theory, a stringent test of the
actual generation of a fermion mass term of non-perturbative origin. A soft
twisted fermion mass term is introduced to circumvent the problem of
exceptional configurations, and observables are then calculated in the limit of
vanishing twisted mass.
