Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions

Abstract

We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{Y}$ theory. Within this model we demonstrate: (1) Strong Yukawa interactions between massless fermion fields and a massive scalar field carrying the axial charge generate dynamically the fermion and boson proper self-energies, which are ultraviolet-finite and chirally noninvariant. (2) Solutions of the underlying Schwinger-Dyson equations found numerically exhibit a huge amplification of the fermion mass ratios as a response to mild changes of the ratios of the Yukawa couplings. (3) The ``would-be'' Nambu-Goldstone boson is a composite of both the fermion and scalar fields, and it gives rise to the mass of the axial-vector gauge boson. (4) Spontaneous breakdown of the gauge symmetry further manifests by mass splitting of the complex scalar and by new symmetry-breaking vertices, generated at one loop. In particular, we work out in detail the cubic vertex of the Abelian gauge boson.