"Super"-Dilatation Symmetry of the Top-Higgs System

TL;DR

This paper uncovers a novel symmetry in the top-Higgs system that relates couplings at a high energy scale, suggesting a new physics scale and explaining the mass relationship between the top quark and Higgs boson.

Contribution

It introduces an exact (up to total divergences) supersymmetric-like symmetry in the top-Higgs system, linking the Higgs quartic and top Yukawa couplings at a high energy scale.

Findings

Identifies a symmetry involving shifts and mixing of top and Higgs fields.

Derives a relationship  =  g^2 between couplings at a few TeV scale.

Explains the mass of the top quark and Higgs in the symmetric and broken phases.

Abstract

The top-Higgs system, consisting of top quark (LH doublet, RH singlet), and Higgs boson kinetic terms, with gauge fields set to zero, has an exact (modulo total divergences) symmetry where both fermion and Higgs fields are shifted and mixed in a supersymmetric fashion. The full Higgs-Yukawa interaction and Higgs-potential, including additional 1/\Lambda^2 N JL-like interactions, also has this symmetry to 0(1/\Lambda^4) up to null-operators. Thus the interaction lagrangian can be viewed as a power series in 1/\Lambda^2. The symmetry involves interplay of the Higgs quartic interaction with the Higgs-Yukawa interaction and implies the relationship, \lambda = \half g^2 between the top--Yukawa coupling, g, and Higgs quartic coupling, \lambda, at a high energy scale \Lambda = few TeV. We interpret this to be a new physics scale. The top quark is massless in the symmetric phase, satisfying the Nambu-Goldstone theorem. The fermionic shift part of the current is \propto (1-H^\dagger H/v^2), owing to the interplay of \lambda and g, and vanishes in the broken phase. Hence the Nambu-Goldstone theorem is trivially evaded in the broken phase and the top quark becomes heavy (it is not a Goldstino). We have m_t=m_h,subject to radiative corrections that can in principle pull the Higgs into concordance with experiment.