Phase structure of the Higgs-Yukawa systems with chirally invariant lattice fermion actions

TL;DR

This paper develops an analytical mean field approach to study the phase structure of lattice Higgs-Yukawa systems with various symmetry groups and fermion actions, identifying conditions for non-trivial fixed points relevant to continuum physics.

Contribution

It introduces a variational mean field method for analyzing phase diagrams of lattice Higgs-Yukawa models with chirally invariant fermions, highlighting the dependence on symmetry and action form.

Findings

Phase diagrams depend on symmetry group and fermion action.

Non-trivial fixed points may exist only in specific models.

Candidates for continuum physics fixed points identified in certain systems.

Abstract

We develop analytical technique for examining phase structure of $Z_2$, $U(1)$, and $SU(2)$ lattice Higgs-Yukawa systems with radially frozen Higgs fields and chirally invariant lattice fermion actions. The method is based on variational mean field approximation. We analyse phase diagrams of such systems with different forms of lattice fermion actions and demonstrate that it crucially depends both on the symmetry group and on the form of the action. We discuss location in the diagrams of possible non-trivial fixed points relevant to continuum physics, and argue that the candidates can exist only in $Z_2$ system with SLAC action and $U(1)$ systems with naive and SLAC actions. [Note: By a product, missing term in Eq. (3.5) of hep-lat/9309010 is reconstructed, that, however, affects only the result of Sect. 4.3 (Fig. 3) of that reference (cf. Fig. 2(c) of this paper).]