Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

TL;DR

This paper proposes a lattice framework to non-perturbatively investigate fermion mass generation in a gauge-fermion-scalar model, using Ward identities to identify critical couplings and test mass generation mechanisms.

Contribution

It introduces a lattice setup with Wilson-like terms to study non-perturbative fermion mass generation, employing Ward identities in quenched approximation.

Findings

Determination of the critical Yukawa coupling in the Wigner phase.

Evidence supporting non-perturbative fermion mass generation in the Nambu-Goldstone phase.

Validation of the lattice approach using Ward identities and twisted mass techniques.

Abstract

In this contribution we lay down a lattice setup that allows for the non-perturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an "irrelevant" Wilson-like term. Using naive fermions in quenched approximation and based on the renormalized Ward identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in the Wigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.