Abstract
In this contribution we lay down a lattice setup that allows for the nonperturbative 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 renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner 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.
Highlights
In [1] a new non-perturbative (NP) mechanism for elementary particle mass generation was conjectured
The Lagrangian (1) describes a SU(2) fermion doublet subjected to non-Abelian gauge interaction and coupled to a complex scalar field via Wilson-like (eq (4)) and Yukawa (eq (5)) terms
In the equations above we have introduced the covariant derivatives
Summary
The Lagrangian (1) describes a SU(2) fermion doublet subjected to non-Abelian gauge interaction and coupled to a complex scalar field via Wilson-like (eq (4)) and Yukawa (eq (5)) terms. In the Wigner phase no NP terms (i.e. ellipses) are expected to occur in the mixing pattern of eq (11) and the transformations χ L leads to eq (12) without the ellipses [1]. In the Nambu-Goldstone phase a non-perturbative term is expected/conjectured [1] to appear in the mixing pattern of eqs. Occurrence of the c1Λs term in the (13) implies the presence of c1ΛsΨ Ψ term in ΓlNoGc , the local effective action in the NG phase This term describe NP breaking of χ L⊗χR and in particular gives fermions a mass c1Λs. It is worth noticing that if the mechanism we have conjectured really exists it will generate a NP mass term for the fermions even in the quenched approximation where the vertices (b) and (c) of fig. 1, and the two rightmost diagrams of fig. 2, are still present
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