Perturbative spectrum of a Yukawa-Higgs model with Ginsparg-Wilson fermions

TL;DR

This paper analyzes a lattice Yukawa-Higgs model with Ginsparg-Wilson fermions, revealing that gauge bosons become massive via spontaneous symmetry breaking, resulting in a spectrum of massless fermions, massive fermions, and massive vector bosons.

Contribution

It demonstrates that gauge bosons always acquire mass through the St"uckelberg mechanism in this model, regardless of interaction strength, providing insight into lattice chiral gauge theories.

Findings

Gauge bosons become massive via the Higgs mechanism.

The physical spectrum includes massless fermions, massive fermions, and massive vector bosons.

Gauge symmetry is spontaneously broken in the model.

Abstract

A Yukawa-Higgs model with Ginsparg-Wilson (GW) fermions, proposed recently by Bhattacharya, Martin and Poppitz as a possible lattice formulation of chiral gauge theories, is studied. A simple argument shows that the gauge boson always acquires mass by the St\"uckelberg (or, in a broad sense, Higgs) mechanism, regardless of strength of interactions. The gauge symmetry is spontaneously broken. When the gauge coupling constant is small, the physical spectrum of the model consists of massless fermions, massive fermions and \emph{massive} vector bosons.