SEARCH FOR AN UPPER BOUND OF THE RENORMALIZED YUKAWA COUPLING IN A LATTICE FERMION HIGGS-MODEL

We study the scaling laws for the fermion mass and the scalar field expectation value in the weak coupling region of the broken phase of a lattice regularized chiral-invariant SU(2)L x SU(2)R fermion-Higgs model with bare Yukawa coupling y and Wilson-Yukawa coupling w. In particular we concentrate on the region in the vicinity of the line A, which is the line of maximal values of y + 4w on the critical surface containing the gaussian fixed point. We have not found any indication for the existence of a nontrivial fixed point on that line or anywhere else in the weak coupling region. The renormalized Yukawa coupling y(R) as a function of the fermionic correlation length appears to be bounded from above. The upper bound obtained from the numerical data at w = 0 is compatible with the perturbative unitarity bound. Furthermore, in the weak coupling region, including the line A. it is not possible to choose w such that the unwanted fermion doublers would be removed from the physical particle spectrum.