Abstract
Based on a recent proposal according to which elementary particle masses could be generated by a non-perturbative dynamical phenomenon, alternative to the Higgs mechanism, we carry out lattice simulations of a model where a non-abelian strongly interacting fermion doublet is also coupled to a doublet of complex scalar fields via a Yukawa and an “irrelevant" Wilson-like term. In this pioneering study we use naive fermions and work in the quenched approximation. We present preliminary numerical results both in the Wigner and in the Nambu-Goldstone phase, focusing on the observables relevant to check the occurrence of the conjectured dynamical fermion mass generation effect in the continuum limit of the critical theory in its spontaneously broken phase.
Highlights
1 Introduction In Refs. [1, 2] a novel approach to the mass generation of elementary particles and the mass hierarchy problem has been proposed. It is based on a Non-Perturbative (NP) mechanism whose existence can be tested by studying, with the help of Lattice QCD (LQCD) simulations, the properties of a nonAbelian (SU(3) gauge) toy-model where an isospin doublet of strongly interacting fermions is coupled to a complex scalar field via Yukawa and Wilson-like terms
We have discussed a toy-model that exemplifies a novel NP mechanism proposed in Ref. [1] for dynamical fermion mass generation
The fundamental property of the mechanism consists in the enhancement of the QCD symmetries in such a way that fermion masses emerge in a natural way [11], being independent from the Yukawa interaction and the scalar field
Summary
We denote with ΨL = (uL dL)T and ΨR = (uR dR)T the fermion iso-doublets. The Yukawa and Wilson-like terms are given by Eqs. The Yukawa coupling and the Wilson-like parameter are denoted by η and ρ, respectively. The scalar field Φ = (φ, −iτ2φ∗) is a 2 × 2 matrix with φ an iso-doublet of complex scalar fields. It obeys a quartic scalar potential denoted by the term V(Φ) of eq (3) where μ20 and λ0 are, respectively, the (bare) values for the squared mass and the self-interaction coupling constant of the scalar field. On-going work on the toy-model has been reported in Ref. [4]
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