Origin of Mass - Horizons Expanding from the Nambu's Theory

TL;DR

This paper explores the origin of mass through strong dynamics, showing how the Standard Model Higgs can be viewed as a pseudo-dilaton within scale-invariant nonlinear sigma models, linking it to theories like technicolor and top condensates.

Contribution

It demonstrates the equivalence of the SM Higgs Lagrangian to a scale-invariant nonlinear sigma model and Hidden Local Symmetry, providing a unified perspective on mass origin from strong dynamics.

Findings

The SM Higgs can be expressed as a (pseudo-) dilaton in a scale-invariant nonlinear sigma model.

The Higgs Lagrangian is gauge equivalent to a scale-invariant Hidden Local Symmetry (s-HLS) model.

The top quark condensate and walking technicolor models can be described within this framework, identifying the Higgs as a dilaton.

Abstract

Origin of mass may be strong dynamics of matter in the vacuum. Since the initial proposal of Nambu for the origin of the nucleon mass, the dynamical symmetry breaking in the strongly coupled underlying theories has been expanding the horizons in the context of the modern version of the origin of mass beyond the Standard Model (SM). The Nambu-Jona-Lasinio (NJL) model is a typical strong coupling theory with the non-zero critical coupling, in sharp contrast to its precedent model, the Bardeen-Cooper-Schrieffer theory for the superconductor. The non-zero critical coupling is also hidden in the asymptotically free gauge theories including QCD and walking technicolor. As is well known, the NJL model can be cast into the SM Higgs Lagrangian. We show that the SM Higgs Lagrangian is simply rewritten into a form of the (approximately) scale-invariant nonlinear sigma model, with both the chiral symmetry and scale symmetry realized nonlinearly, with the SM Higgs being nothing but the (pseudo-) dilaton. The SM Higgs Lagrangian is further gauge equivalent to the scale-invariant Hidden Local Symmetry (HLS) Lagrangian, s-HLS, having spin 1 bosons hidden in the SM. As the simplest possible underlying theory for the SM Higgs Lagrangian we first discuss the top quark condensate ("top-mode SM"), where the top-mode dilaton is the 125 GeV Higgs. We then discuss the walking technicolor having near infrared conformality, whose effective theory is the s-HLS model precisely the same as the SM Higgs Lagrangian (with larger chiral symmetry), where the 125 GeV Higgs is successfully identified with the techidilaton.