NUCLEAR Nuclear Physics B 371 (1992) 683—712 P H VS I C S B North-Holland _______________ Search for an upper bound of the renormalized Yukawa coupling in a lattice fermion—Higgs model * Wolfgang Bock 1,2 Asit K. De 1,2 Christoph Frick 2,1 Karl Jansen ~ and Thomas Trappenberg 1,2 1lnstitut für Theoretische Physik E, RWI’HAachen, D-5100 Aachen, Germany 2HLP~c/o KFA Jülich, P.O. Box 1913, D-5l7OJülich, Germany ~ UCSD, Department of Physics B-019, La Jolla, CA 92093, USA Received 11 June 1991 Accepted for publication 7 October 1991 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® 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 YR 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. 1. Introduction In the last three years nonperturbative investigations of Yukawa models by means of the lattice regularization method have received a lot of attention [1—3]. At the beginning these studies were mainly motivated by the following two complexes of nonperturbative questions [4]:(i) At large values of the bare Yukawa coupling ya nontrivial fixed point might exist at which an interacting continuum limit can be constructed. The existence of such a nontrivial fixed point in a 4-dimensional lattice field theory would be of great interest since at present all the known examples seem to support the fact that any nonasymptotically free field * Supported by the Deutsche Forschungsgemeinschaft 0550-3213/92/$05.00 © 1992 — Elsevier Science Publishers B.V. All rights reserved