# 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:

- Department of Theoretical Physics, Nuclear Physics Institute, Rez (Prague) (Czech Republic)
- (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}

}