Which Higgs-Yukawa systems can posses non-trivial fixed points

Abstract

We argue that non-trivial fixed points bordering on the paramagnetic and ferromagnetic phases are most likely to exist in the Higgs-Yukawa systems that have a connected domain with the paramagnetic phase and no ferrimagnetic phase. We find three examples of such systems; among them is the U(1) system with naive fermions.1. In this talk we want to emphasize the following three points:(i) that the phase structure of the HiggsYukawa systems depend crucially both on on their symmetry group and on the form of the lattice fermion action, even though the coupling of the fermions to the Higgs fields is the same;(ii) that the most likely candidates for the systems with non-trivial fixed points bordering on the paramagnetic (PM) and ferromagnetic (FM) phases are the systems that have a connected domain with the PM phase and no ferrimagnetic (FI) phase;(iii) that one of such systems is the U(1) system with naive fermions.We investigate the phase diagrams of the Z 2 , U(1) and SU(2) Higgs-Yukawa systems with radially frozen Higgs fields for three types of chirally invariant lattice fermion actions. Our method is based on the variational mean field approximation, where contribution of the fermion determinant is calculated for weak and strong Yukawa coupling regimes in a certain ladder approximation [1,2]. The action of the systemhas two parameters: the scalar hopping parameter κ and the Yukawa coupling y; φ a are real components of the group-valued field Φ,Φ = P L Φ † + P R Φ. Given group, the system is determined by the form of the lattice Dirac operator D. At κ > 0 it corresponds to certain continuum Higgs-Yukawa model; at non-positive κ such a correspondence is distroyed. We shall require the system to be chirally invariant and operator D to have the form:We consider three examples of the lattice fermions satisfying these conditions: naive fermions withnon-local SLAC fermions withand fermions withwhose action although is non-local, is originated from the local mirror fermion action after integrating out the mirror fermions (see [3] and also [2]). In all the cases the fermions couple to the Higgs fields in the same way.3. The method [1,2] yields closed analytical expressions for the critical lines κ(y) between the FM and PM phases and between the antiferromagnetic (AM) and PM phases in the weak