Non-perturbative generation of elementary fermion masses: a numerical study

TL;DR

This study uses lattice simulations of an SU(3) gauge model with fermions and scalars to demonstrate non-perturbative generation of finite fermion masses, avoiding UV divergences through an exact symmetry.

Contribution

It provides the first numerical evidence that a UV finite fermion mass can be generated non-perturbatively in a lattice gauge theory with specific symmetries and operators.

Findings

Evidence of non-perturbative fermion mass generation.

Fermion masses are UV finite and generated without divergences.

The model maintains an exact symmetry preventing UV power divergences.

Abstract

In this talk we present a numerical lattice study of an SU(3) gauge model where an SU(2) doublet of non-Abelian strongly interacting fermions is coupled to a complex scalar field doublet via a Yukawa and a Wilson-like term. The model enjoys an exact symmetry, acting on all fields, which prevents UV power divergent fermion mass corrections, despite the presence of these two chiral breaking operators in the Lagrangian. In the phase where the scalar potential is non-degenerate and fermions are massless, the bare Yukawa coupling can be set at a critical value at which chiral fermion transformations become symmetries of the theory. Numerical simulations in the Nambu-Goldstone phase of the critical theory, for which the renormalized Yukawa coupling by construction vanishes, give evidence for non-perturbative generation of a UV finite fermion mass term in the effective action.