The Higgs Boson Mass and Ward-Takahashi Identity in Gauged Nambu-Jona-Lasinio Model

TL;DR

This paper derives a new formula for the composite Higgs boson mass using Ward-Takahashi identity and Schwinger-Dyson equations, providing results consistent with existing approaches and applying it to QCD.

Contribution

It introduces a novel formula for the Higgs mass based on Ward-Takahashi identity, improving understanding of composite Higgs in gauged Nambu-Jona-Lasinio models.

Findings

For constant gauge coupling, M_H ≈ √2 M, consistent with other approaches.

For running gauge coupling, M_H ≈ 2√((A-1)/(2A-1)) M.

Application to QCD suggests M_σ ≈ √2 M_{dyn}.

Abstract

A new formula for the composite Higgs boson mass is given, based on the Ward-Takahashi identity and the Schwinger-Dyson(SD) equation. In this formula the dominant asymptotic solution of the SD equation yields a correct answer, in sharp contrast to the Partially Conserved Dilatation Current(PCDC) approach where the sub- and sub-sub-dominant solutions should be taken into account carefully. In the gauged Nambu-Jona-Lasinio model we find M_H \simeq \sqrt{2}M for the composite Higgs boson mass M_H and the dynamical mass of the fermion M in the case of the constant gauge coupling(with large cut off), which is consistent with the PCDC approach and the renormalization-group approach. As to the case of the running gauge coupling, we find M_H \simeq 2 \sqrt{(A-1)/(2A-1)}M, where A \equiv 18 C_2 /(11N_c - 2N_f) with C_2 being the quadratic Casimir of the fermion representation. We also discuss a straightforward application of our formula to QCD(without 4-Fermi coupling), which yields M_{\sigma} \sim \sqrt{2}M_{dyn}, with M_{\sigma} and M_{dyn} being the light scalar(``\sigma-meson'') mass and mass of the constituent quark, respectively.