# Chiral perturbation theory for the quenched approximation of QCD

## Abstract

We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a Lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in {ital f}{sub {ital K}}/{ital f}{sub {pi}}, {ital m}{sub {pi}}, {ital m}{sub {ital K}}, and the ratio of {l angle}{ital {bar s}s}{r angle} to {l angle}{ital {bar u}u}{r angle}. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.

- Authors:

- (Department of Physics, Washington University, St. Louis, Missouri 63130 (United States))

- Publication Date:

- OSTI Identifier:
- 7183948

- DOE Contract Number:
- AC02-78ER04915

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D (Particles Fields); (United States)

- Additional Journal Information:
- Journal Volume: 46:2; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; PERTURBATION THEORY; ALGORITHMS; CHIRALITY; FERMIONS; FEYNMAN DIAGRAM; GOLDSTONE BOSONS; LAGRANGIAN FUNCTION; MATRIX ELEMENTS; MESON-MESON INTERACTIONS; PROPAGATOR; PSEUDOSCALAR MESONS; SCATTERING; BOSONS; DIAGRAMS; ELEMENTARY PARTICLES; FIELD THEORIES; FUNCTIONS; HADRON-HADRON INTERACTIONS; HADRONS; INTERACTIONS; MATHEMATICAL LOGIC; MESONS; PARTICLE INTERACTIONS; PARTICLE PROPERTIES; POSTULATED PARTICLES; QUANTUM FIELD THEORY; 662230* - Quantum Chromodynamics- (1992-); 662340 - Hadron Interactions- (1992-)

### Citation Formats

```
Bernard, C.W., and Golterman, M.F.L..
```*Chiral perturbation theory for the quenched approximation of QCD*. United States: N. p., 1992.
Web. doi:10.1103/PhysRevD.46.853.

```
Bernard, C.W., & Golterman, M.F.L..
```*Chiral perturbation theory for the quenched approximation of QCD*. United States. doi:10.1103/PhysRevD.46.853.

```
Bernard, C.W., and Golterman, M.F.L.. Wed .
"Chiral perturbation theory for the quenched approximation of QCD". United States. doi:10.1103/PhysRevD.46.853.
```

```
@article{osti_7183948,
```

title = {Chiral perturbation theory for the quenched approximation of QCD},

author = {Bernard, C.W. and Golterman, M.F.L.},

abstractNote = {We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a Lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in {ital f}{sub {ital K}}/{ital f}{sub {pi}}, {ital m}{sub {pi}}, {ital m}{sub {ital K}}, and the ratio of {l angle}{ital {bar s}s}{r angle} to {l angle}{ital {bar u}u}{r angle}. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.},

doi = {10.1103/PhysRevD.46.853},

journal = {Physical Review, D (Particles Fields); (United States)},

issn = {0556-2821},

number = ,

volume = 46:2,

place = {United States},

year = {1992},

month = {7}

}