# Clebsch-Gordan construction of lattice interpolating fields for excited baryons

## Abstract

Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 842854

- Report Number(s):
- JLAB-THY-05-397; DOE/ER/40150-3562

TRN: US0503795

- DOE Contract Number:
- AC05-84ER40150

- Resource Type:
- Journal Article

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BARYONS; CLEBSCH-GORDAN COEFFICIENTS; CONSTRUCTION; FIELD OPERATORS; IRREDUCIBLE REPRESENTATIONS; ISOSPIN; ORBITAL ANGULAR MOMENTUM; QUANTUM CHROMODYNAMICS; QUARKS; SPINORS; STRANGENESS; SYMMETRY

### Citation Formats

```
S. Basak, R. Edwards, G. Fleming, U. Heller, C. Morningstar, D. Richards, I. Sato, and S. Wallace.
```*Clebsch-Gordan construction of lattice interpolating fields for excited baryons*. United States: N. p., 2005.
Web.

```
S. Basak, R. Edwards, G. Fleming, U. Heller, C. Morningstar, D. Richards, I. Sato, & S. Wallace.
```*Clebsch-Gordan construction of lattice interpolating fields for excited baryons*. United States.

```
S. Basak, R. Edwards, G. Fleming, U. Heller, C. Morningstar, D. Richards, I. Sato, and S. Wallace. Mon .
"Clebsch-Gordan construction of lattice interpolating fields for excited baryons". United States. https://www.osti.gov/servlets/purl/842854.
```

```
@article{osti_842854,
```

title = {Clebsch-Gordan construction of lattice interpolating fields for excited baryons},

author = {S. Basak and R. Edwards and G. Fleming and U. Heller and C. Morningstar and D. Richards and I. Sato and S. Wallace},

abstractNote = {Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum SU(2) group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2005},

month = {8}

}