Composite antisymmetric-tensor Nambu-Goldstone bosons in a four-fermion interaction model and the Higgs mechanism

TL;DR

This paper demonstrates that in a four-fermion interaction model derived from the 't Hooft interaction, antisymmetric tensor Nambu-Goldstone bosons emerge under specific coupling ratios, leading to massive non-Abelian gauge bosons without axial-vector mixing.

Contribution

It shows the natural emergence of antisymmetric tensor Nambu-Goldstone bosons and gauge boson mass generation within a four-fermion interaction framework based on the 't Hooft interaction.

Findings

Antisymmetric tensor Nambu-Goldstone bosons appear at a 2:1 scalar to tensor coupling ratio.

Non-Abelian gauge bosons acquire mass without axial-vector mixing.

The coupling ratio aligns with the Fierz transform of the 't Hooft interaction.

Abstract

Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with antisymmetric Lorentz tensor interaction terms augmented by an NJL type Lorentz scalar inetraction responsible for dynamical symmetry breaking and quark mass generation), we show that: (1) antisymmetric tensor Nambu-Goldstone bosons appear provided that the scalar and tensor couplings stand in the proportion of two to one, which ratio appears naturally in the Fierz transform of the two-flavour 't Hooft interaction; (2) non-Abelian vector gauge bosons coupled to this system acquire a non-zero mass. Axial-vector fields do not mix with antisymmetric tensor fields, so there is no mass shift there.