Mass Gap in U(1) Higgs-Yukawa model on a unit lattice

TL;DR

This paper provides a non-perturbative proof that fermions acquire mass through the Higgs mechanism in a U(1) Higgs-Yukawa model, demonstrating a mass gap via exponential decay of correlation functions.

Contribution

It offers the first non-perturbative proof of mass generation in a U(1) Higgs-Yukawa model on a lattice, establishing the existence of a mass gap.

Findings

Fermionic correlation functions decay exponentially, indicating massive fermions.

The Higgs boson, photon, and fermion all have non-zero physical masses.

The theory exhibits a mass gap in four dimensions.

Abstract

A non perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs-Yukawa theory on a unit lattice in $d=4$. This decay implies that the Higgs boson, the photon and the fermion all have a non zero physical mass and the theory is said to have a mass gap.