Incorporating fermions in the Gaussian Effective Potential: the Higgs-Top Sector

TL;DR

This paper develops a non-perturbative variational approach incorporating fermions into the Gaussian Effective Potential to study the Higgs-Top sector, revealing deviations from scaling, vacuum stability, and analytical results for key observables.

Contribution

It introduces a novel variational extension of the Gaussian Effective Potential that includes fermions, providing new insights into the Higgs-Top model beyond perturbation theory.

Findings

Scaling behavior at strong Yukawa coupling

Vacuum stability for all Yukawa couplings

Analytical expressions for Higgs mass and wave function renormalization

Abstract

The Higgs-Top model is studied by a non-perturbative variational extension of the Gaussian Effective Potential that incorporates fermions. In the limit of a very strong Yukawa coupling the one-loop result is shown to follow a single-parameter scaling while the gaussian fluctuations give rise to important deviations from scaling and to a reduction of the vev and of the top mass. A good general agreement is found with lattice data when a comparison can be made. The vacuum is shown to be stable for any choice of the Yukawa coupling, at variance with renormalized perturbation theory. Analytical results are provided for few observables like the renormalized mass of the Higgs boson and its wave function renormalization constant. Extensions to gauge theories like QCD are briefly discussed.