# Worldline calculation of the three-gluon vertex

## Abstract

The three-gluon vertex is a basic object of interest in nonabelian gauge theory. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in terms of field strength tensors. We verify its equivalence with previously obtained representations, and explain the relation of its structure to the low-energy effective action. The sum rule found by Binger and Brodsky for the scalar, spinor and gluon loop contributions in the present approach relates to worldline supersymmetry.

- Authors:

- Dipartimento di Fisica, Universita di Bologna and INFN Sezione di Bologna Via Irnerio 46, I-40126 Bologna (Italy)
- (Mexico)

- Publication Date:

- OSTI Identifier:
- 22075667

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1492; Journal Issue: 1; Conference: QCD-WORK 2012: International workshop on quantum chromodynamics: Theory and experiment, Lecce (Italy), 18-21 Jun 2012; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; FEYNMAN DIAGRAM; GAUGE INVARIANCE; GLUONS; QUANTUM FIELD THEORY; SCALARS; SUM RULES; SUPERSYMMETRY; TENSORS

### Citation Formats

```
Ahmadiniaz, N., Schubert, C., and Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Apdo. Postal 2-82 C.P. 58040, Morelia, Michoacan.
```*Worldline calculation of the three-gluon vertex*. United States: N. p., 2012.
Web. doi:10.1063/1.4763517.

```
Ahmadiniaz, N., Schubert, C., & Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Apdo. Postal 2-82 C.P. 58040, Morelia, Michoacan.
```*Worldline calculation of the three-gluon vertex*. United States. doi:10.1063/1.4763517.

```
Ahmadiniaz, N., Schubert, C., and Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Apdo. Postal 2-82 C.P. 58040, Morelia, Michoacan. Tue .
"Worldline calculation of the three-gluon vertex". United States. doi:10.1063/1.4763517.
```

```
@article{osti_22075667,
```

title = {Worldline calculation of the three-gluon vertex},

author = {Ahmadiniaz, N. and Schubert, C. and Instituto de Fisica y Matematicas Universidad Michoacana de San Nicolas de Hidalgo Apdo. Postal 2-82 C.P. 58040, Morelia, Michoacan},

abstractNote = {The three-gluon vertex is a basic object of interest in nonabelian gauge theory. At the one-loop level, it has been calculated and analyzed by a number of authors. Here we use the worldline formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in terms of field strength tensors. We verify its equivalence with previously obtained representations, and explain the relation of its structure to the low-energy effective action. The sum rule found by Binger and Brodsky for the scalar, spinor and gluon loop contributions in the present approach relates to worldline supersymmetry.},

doi = {10.1063/1.4763517},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1492,

place = {United States},

year = {2012},

month = {10}

}

DOI: 10.1063/1.4763517

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