Dynamically Broken U(1) `Left' Gauge Theories in Four Dimensions

TL;DR

This paper investigates a dynamically broken U(1) gauge theory with a composite scalar doublet, demonstrating anomaly cancellation, gauge current conservation, and renormalizability within the Nambu-Jona-Lasinio approximation, ensuring unitarity.

Contribution

It introduces a novel U(1) gauge theory with a composite scalar, analyzing its symmetry breaking, anomaly cancellation, and renormalizability in a new framework.

Findings

Anomaly disappears after symmetry breaking.

Gauge current remains conserved.

Theory is renormalizable and unitary.

Abstract

We study a dynamically broken U(1) "left" gauge theory endowed with a composite scalar doublet (one scalar and one pseudoscalar); its Lagrangian only differs from that of an abelian `Standard Model' by the addition of a derivative coupling between a Wess-Zumino field, linked to the previous scalars, and the fermionic current. Yet, in the Feynman path integral, the non independence of the fermionic and scalar variables of integration requires the introduction of constraints. When the gauge symmetry is broken by the vacuum expectation value of the scalar field, they freeze all degrees of freedom but those of a massive gauge field, including a (abelian) pion. The anomaly disappears and the gauge current is conserved. This is shown, and renormalizability studied, in the `Nambu-Jona-Lasinio approximation'. Unitarity is demonstrated on general grounds.