# Complete O(v{sup 2}) corrections to the static interquark potential from SU(3) gauge theory

## Abstract

For the first time, we determine the complete spin- and momentum-dependent order v{sup 2} corrections to the static interquark potential from simulations of QCD in the valence quark approximation at inverse lattice spacings of 2{endash}3 GeV. A new flavor-dependent correction to the central potential is found. We report an r{sup {minus}2} contribution to the long range spin-orbit potential V{sub 1}{sup {prime}}. The other spin-dependent potentials turn out to be short ranged and can be well understood by means of perturbation theory. The momentum-dependent potentials qualitatively agree with minimal area law expectations. In view of spectrum calculations, we discuss the matching of the effective nonrelativistic theory to QCD as well as renormalization of lattice results. In a first survey of the resulting bottomonia and charmonia spectra we reproduce the experimental levels within average errors of 12.5 MeV and 22 MeV, respectively. {copyright} {ital 1997} {ital The American Physical Society}

- Authors:

- Department of Physics, The University of Southampton, Highfield, Southampton SO17 1BJ (England)
- HLRZ, Forschungszentrum Juelich, D-52425 Juelich and DESY, D-22603 Hamburg (Germany)|[Fachbereich Physik, Bergische Universitaet, Gesamthochschule Wuppertal, Gausstrasse 20, 42097 Wuppertal (Germany)

- Publication Date:

- OSTI Identifier:
- 538693

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review, D

- Additional Journal Information:
- Journal Volume: 56; Journal Issue: 5; Other Information: PBD: Sep 1997

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; QUANTUM CHROMODYNAMICS; POTENTIALS; MESONS; LATTICE FIELD THEORY; BAG MODEL; UNIFIED GAUGE MODELS; SU-3 GROUPS; QUARKS; CORRECTIONS; SPIN; FLAVOR; PERTURBATION THEORY; SPECTRA; RENORMALIZATION; CHARMONIUM; BOTTOMONIUM; SIMULATION

### Citation Formats

```
Bali, G.S., Schilling, K., and Wachter, A..
```*Complete O(v{sup 2}) corrections to the static interquark potential from SU(3) gauge theory*. United States: N. p., 1997.
Web. doi:10.1103/PhysRevD.56.2566.

```
Bali, G.S., Schilling, K., & Wachter, A..
```*Complete O(v{sup 2}) corrections to the static interquark potential from SU(3) gauge theory*. United States. doi:10.1103/PhysRevD.56.2566.

```
Bali, G.S., Schilling, K., and Wachter, A.. Mon .
"Complete O(v{sup 2}) corrections to the static interquark potential from SU(3) gauge theory". United States. doi:10.1103/PhysRevD.56.2566.
```

```
@article{osti_538693,
```

title = {Complete O(v{sup 2}) corrections to the static interquark potential from SU(3) gauge theory},

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

abstractNote = {For the first time, we determine the complete spin- and momentum-dependent order v{sup 2} corrections to the static interquark potential from simulations of QCD in the valence quark approximation at inverse lattice spacings of 2{endash}3 GeV. A new flavor-dependent correction to the central potential is found. We report an r{sup {minus}2} contribution to the long range spin-orbit potential V{sub 1}{sup {prime}}. The other spin-dependent potentials turn out to be short ranged and can be well understood by means of perturbation theory. The momentum-dependent potentials qualitatively agree with minimal area law expectations. In view of spectrum calculations, we discuss the matching of the effective nonrelativistic theory to QCD as well as renormalization of lattice results. In a first survey of the resulting bottomonia and charmonia spectra we reproduce the experimental levels within average errors of 12.5 MeV and 22 MeV, respectively. {copyright} {ital 1997} {ital The American Physical Society}},

doi = {10.1103/PhysRevD.56.2566},

journal = {Physical Review, D},

number = 5,

volume = 56,

place = {United States},

year = {1997},

month = {9}

}