Fermion mass in the Wilson-Yukawa approach for chiral Yukawa theory

We consider a modification of the Wilson-Yukawa model to overcome its difficulty that the fermion mass is not proportional to the Higgs vacuum expectation value. In the modification scalar and fermionic regulator fields are introduced so that all the physical fermion fields possess shift symmetry when the Yukawa coupling vanishes. With the fermionic hopping parameter expansion it is shown that the fermion mass is proportional to the Higgs vacuum expectation value and that the coupling of fermion to the external gauge field can be chiral if the hopping parameter of the scalar regulator field is taken to the critical value.