# Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory

## Abstract

We present results on the static {ital q{bar q}} potential from high-statistics simulations on 16{sup 4}, 24{sup 3}{times}32, and 32{sup 4} lattices, using the standard Wilson action at {beta}=6.0, 6.2, and 6.4 on the Connection Machine CM2. To decrease noise and increase accuracy, we applied a suitable local smoothing technique on the spatial parts of Wilson loop operators. As a result, we find a violation of asymptotic scaling of the string tension, as signaled by {radical}{sigma} /{Lambda}{sub {ital L}}=96.7(1.6)(2.6), 86.4(1.0)(1.9), 82.3(0.8)(1.7), for the three {beta} values, with statistical and systematic errors. We observe a linear confining potential up to distances of 2 fm. A volume of (1.5 fm){sup 3} appears to be sufficient to avoid finite-size effects within our statistical accuracy ({approx}1%).

- Authors:

- (Physics Department, Bergische Universitaet, Gesamthochschule Wuppertal, Gauss Strasse 20, 5600 Wuppertal (Germany))

- Publication Date:

- OSTI Identifier:
- 7084121

- Alternate Identifier(s):
- OSTI ID: 7084121

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 46:6; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LATTICE FIELD THEORY; QUARK-ANTIQUARK INTERACTIONS; POTENTIALS; CORRELATION FUNCTIONS; EUCLIDEAN SPACE; GAUGE INVARIANCE; MATRIX ELEMENTS; QUANTUM CHROMODYNAMICS; SCALING LAWS; SIMULATION; STATISTICAL MECHANICS; STRING MODELS; SU-2 GROUPS; SU-3 GROUPS; VARIATIONAL METHODS; WILSON LOOP; COMPOSITE MODELS; EXTENDED PARTICLE MODEL; FIELD THEORIES; FUNCTIONS; INTERACTIONS; INVARIANCE PRINCIPLES; LIE GROUPS; MATHEMATICAL MODELS; MATHEMATICAL SPACE; MECHANICS; PARTICLE INTERACTIONS; PARTICLE MODELS; QUANTUM FIELD THEORY; QUARK MODEL; RIEMANN SPACE; SPACE; SU GROUPS; SYMMETRY GROUPS 662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-); 662120 -- General Theory of Particles & Fields-- Symmetry, Conservation Laws, Currents & Their Properties-- (1992-); 662230 -- Quantum Chromodynamics-- (1992-); 662340 -- Hadron Interactions-- (1992-)

### Citation Formats

```
Bali, G.S., and Schilling, K.
```*Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory*. United States: N. p., 1992.
Web. doi:10.1103/PhysRevD.46.2636.

```
Bali, G.S., & Schilling, K.
```*Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory*. United States. doi:10.1103/PhysRevD.46.2636.

```
Bali, G.S., and Schilling, K. Tue .
"Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory". United States. doi:10.1103/PhysRevD.46.2636.
```

```
@article{osti_7084121,
```

title = {Static quark-antiquark potential: Scaling behavior and finite-size effects in SU(3) lattice gauge theory},

author = {Bali, G.S. and Schilling, K.},

abstractNote = {We present results on the static {ital q{bar q}} potential from high-statistics simulations on 16{sup 4}, 24{sup 3}{times}32, and 32{sup 4} lattices, using the standard Wilson action at {beta}=6.0, 6.2, and 6.4 on the Connection Machine CM2. To decrease noise and increase accuracy, we applied a suitable local smoothing technique on the spatial parts of Wilson loop operators. As a result, we find a violation of asymptotic scaling of the string tension, as signaled by {radical}{sigma} /{Lambda}{sub {ital L}}=96.7(1.6)(2.6), 86.4(1.0)(1.9), 82.3(0.8)(1.7), for the three {beta} values, with statistical and systematic errors. We observe a linear confining potential up to distances of 2 fm. A volume of (1.5 fm){sup 3} appears to be sufficient to avoid finite-size effects within our statistical accuracy ({approx}1%).},

doi = {10.1103/PhysRevD.46.2636},

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

issn = {0556-2821},

number = ,

volume = 46:6,

place = {United States},

year = {1992},

month = {9}

}