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Title: 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){sub L}xU(1){sub 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.

Authors:
;  [1];  [2];  [1]
  1. Department of Theoretical Physics, Nuclear Physics Institute, Rez (Prague) (Czech Republic)
  2. (Czech Republic)
Publication Date:
OSTI Identifier:
21020105
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevD.75.056003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; FERMIONS; GAUGE INVARIANCE; GOLDSTONE BOSONS; MATHEMATICAL SOLUTIONS; REST MASS; SCALAR FIELDS; SCHWINGER FUNCTIONAL EQUATIONS; SELF-ENERGY; STANDARD MODEL; STRONG INTERACTIONS; SU-2 GROUPS; SYMMETRY BREAKING; U-1 GROUPS; ULTRAVIOLET RADIATION

Citation Formats

Benes, Petr, Brauner, Tomas, Faculty of Mathematics and Physics, Charles University, Prague, and Hosek, Jiri. Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.056003.
Benes, Petr, Brauner, Tomas, Faculty of Mathematics and Physics, Charles University, Prague, & Hosek, Jiri. Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions. United States. doi:10.1103/PHYSREVD.75.056003.
Benes, Petr, Brauner, Tomas, Faculty of Mathematics and Physics, Charles University, Prague, and Hosek, Jiri. Thu . "Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions". United States. doi:10.1103/PHYSREVD.75.056003.
@article{osti_21020105,
title = {Dynamical breakdown of Abelian gauge chiral symmetry by strong Yukawa interactions},
author = {Benes, Petr and Brauner, Tomas and Faculty of Mathematics and Physics, Charles University, Prague and Hosek, Jiri},
abstractNote = {We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2){sub L}xU(1){sub 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.},
doi = {10.1103/PHYSREVD.75.056003},
journal = {Physical Review. D, Particles Fields},
number = 5,
volume = 75,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2007},
month = {Thu Mar 01 00:00:00 EST 2007}
}
  • Two-dimensional Abelian gauge theories with nonstandard fermion content are analyzed. One model contains N fermions with different electric charges and the other has a left-right-asymmetric fermion content. The operator solutions are explicitly constructed in a covariant gauge and a noncovariant gauge. In both models the gauge and the chiral symmetries are broken spontaneously. The direction of this breakdown is dictated by the axial anomaly. The spectrum of the minimal theory consists of one massive boson and one massless boson for both types of theories. It is argued that the left-right-asymmetric model is inappropriate to test the most-attractive-channel hypothesis.
  • We study dynamical mass generation for fermions in the Yukawa and the supersymmetric Wess-Zumino (WZ) models. It is found that above a critical coupling fermion mass can be generated dynamically in the Yukawa model, whereas in the WZ model the fermion does not acquire mass. We also show that the supersymmetry (SUSY) preserving solution is permitted and hence the scalars may not acquire mass either.
  • Chiral-symmetry-breaking parameters are calculated in quenched SU(2) lattice gauge theory and with Abelian gauge fields projected in the maximal Abelian gauge and in the field-strength gauge. Maximal Abelian gauge-projected fields lead to chiral condensate values which are quite similar to those of the full non-Abelian theory. Pseudoscalar and vector meson correlators are calculated and found to be reproduced by the use of maximal Abelian gauge fields for small quark masses. In the field-strength gauge, Abelian-projected fields give a chiral condensate which closely resembles the results of strongly coupled ({beta}{lt}1) gauge theory: the chiral condensate is insensitive to {beta} and themore » quark mass and hence violates scaling badly.« less
  • The SU({ital N}) chiral Schwinger model with a Wess-Zumino term is studied by use of non-Abelian bosonization, the Becchi-Rouet-Stora formalism, and a dual transformation, and it is confirmed that this model is a sensible quantum theory in a certain range of the anomaly parameter {ital a}. The SU({ital N}) gauge symmetry restored by the inclusion of the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. Left-handed fermions are found to be confined while right-handed fermions remain free and massless. For the specific value {ital a}=2, the symmetry of the model enlarges (to a U({ital N}){times}U({ital N}) Kac-Moodymore » symmetry). It is shown by fermionization of the Wess-Zumino field that for {ital a}=2 this model is equivalent to massless two-dimensional QCD (QCD{sub 2}) in the sense that they share the same gauge field and the same left-handed fermions. A dual transformation is used to cast the model into an equivalent nonlinear system of scalar fields only, which reveals the particle spectrum of the model.« less