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

TL;DR

This paper reveals a novel symmetry in the top-Higgs system that relates the top Yukawa coupling and Higgs quartic coupling at a high energy scale, suggesting new physics and explaining the top quark's mass generation.

Contribution

It introduces an exact (up to total divergences) supersymmetric-like symmetry in the top-Higgs system and relates the couplings at a high energy scale, providing insights into top quark mass and Higgs interactions.

Findings

Symmetry relates g and λ at a high scale Λ.

Top quark is massless in the symmetric phase, evading Goldstone theorem.

Predicted m_t ≈ m_h, with potential corrections aligning with experiments.

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 \sim 1/\Lambda^2 NJL-like interactions, also has this symmetry to O(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.