skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effective quark-antiquark potential for the constituent quark model

Abstract

We use Dual QCD to derive an effective potential to order (quark mass)[sup [minus]2] for a constituent quark and antiquark. This is done by expanding the dual QCD Lagrangian to second order in the [ital q[bar q]] spins and velocities around the static central potential, in which the quarks are both spinless and stationary. The field equations are then used to eliminate the dual gluon fields and the Higgs fields of dual QCD in favor of quark variables for an arbitrary but slowly moving [ital q[bar q]] pair with a Dirac string of arbitrary shape connecting them. The result is a Lagrangian, and therefore, a potential, which depends only on the [ital q[bar q]] positions, velocities, and spins. Dual QCD contains only three parameters, which can be determined from the vacuum energy density, the string tension, and the strength of the Coulomb singularity of the central potential. The only free parameters in the spin- and velocity-dependent part of the effective potential are, therefore, the masses of the [ital c] and [ital b] quarks. When inserted into a Schroedinger equation these potentials provide a complete effective constituent quark theory which can be used to calculate [ital q[bar q]] energy levels inmore » terms of the masses and the masses can thereby be fixed (agreement with experiment is excellent). The various potential, spin-spin, spin-orbit, and spinless velocity dependent, can also in principle be compared to lattice calculations of the same quantities. For the spin-orbit case, for example, the agreement is good, although lattice results are not yet precise enough for a real comparison to be made. For the potentials proportional to the velocity squared lattice results do not yet exist. We also attempt to extend the use of these potentials to heavy-light quark-antiquark systems through use of the Salpeter equation and the Dirac equation. The results of this effort are described in two Appendices.« less

Authors:
 [1];  [2];  [3]
  1. University of Washington, Seattle, Washington 98105 (United States)
  2. University of Utah, Salt Lake City, Utah 84112 (United States)
  3. California Institute of Technology, Pasadena, California 91125 (United States)
Publication Date:
OSTI Identifier:
6853253
DOE Contract Number:  
FG03-92ER40701
Resource Type:
Journal Article
Journal Name:
Physical Review, D (Particles Fields); (United States)
Additional Journal Information:
Journal Volume: 51:4; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; QUARK MODEL; POTENTIALS; ANTIPARTICLES; BETHE-SALPETER EQUATION; DIRAC EQUATION; ENERGY DENSITY; FIELD EQUATIONS; GLUONS; HIGGS BOSONS; LAGRANGIAN FUNCTION; QUARKS; SCHROEDINGER EQUATION; SINGULARITY; SPIN; VELOCITY; ANGULAR MOMENTUM; ANTIMATTER; BOSONS; COMPOSITE MODELS; DIFFERENTIAL EQUATIONS; ELEMENTARY PARTICLES; EQUATIONS; FERMIONS; FIELD THEORIES; FUNCTIONS; MATHEMATICAL MODELS; MATTER; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE MODELS; PARTICLE PROPERTIES; POSTULATED PARTICLES; QUANTUM FIELD THEORY; WAVE EQUATIONS; 662240* - Models for Strong Interactions- (1992-)

Citation Formats

Baker, M, Ball, J S, and Zachariasen, F. Effective quark-antiquark potential for the constituent quark model. United States: N. p., 1995. Web. doi:10.1103/PhysRevD.51.1968.
Baker, M, Ball, J S, & Zachariasen, F. Effective quark-antiquark potential for the constituent quark model. United States. doi:10.1103/PhysRevD.51.1968.
Baker, M, Ball, J S, and Zachariasen, F. Wed . "Effective quark-antiquark potential for the constituent quark model". United States. doi:10.1103/PhysRevD.51.1968.
@article{osti_6853253,
title = {Effective quark-antiquark potential for the constituent quark model},
author = {Baker, M and Ball, J S and Zachariasen, F},
abstractNote = {We use Dual QCD to derive an effective potential to order (quark mass)[sup [minus]2] for a constituent quark and antiquark. This is done by expanding the dual QCD Lagrangian to second order in the [ital q[bar q]] spins and velocities around the static central potential, in which the quarks are both spinless and stationary. The field equations are then used to eliminate the dual gluon fields and the Higgs fields of dual QCD in favor of quark variables for an arbitrary but slowly moving [ital q[bar q]] pair with a Dirac string of arbitrary shape connecting them. The result is a Lagrangian, and therefore, a potential, which depends only on the [ital q[bar q]] positions, velocities, and spins. Dual QCD contains only three parameters, which can be determined from the vacuum energy density, the string tension, and the strength of the Coulomb singularity of the central potential. The only free parameters in the spin- and velocity-dependent part of the effective potential are, therefore, the masses of the [ital c] and [ital b] quarks. When inserted into a Schroedinger equation these potentials provide a complete effective constituent quark theory which can be used to calculate [ital q[bar q]] energy levels in terms of the masses and the masses can thereby be fixed (agreement with experiment is excellent). The various potential, spin-spin, spin-orbit, and spinless velocity dependent, can also in principle be compared to lattice calculations of the same quantities. For the spin-orbit case, for example, the agreement is good, although lattice results are not yet precise enough for a real comparison to be made. For the potentials proportional to the velocity squared lattice results do not yet exist. We also attempt to extend the use of these potentials to heavy-light quark-antiquark systems through use of the Salpeter equation and the Dirac equation. The results of this effort are described in two Appendices.},
doi = {10.1103/PhysRevD.51.1968},
journal = {Physical Review, D (Particles Fields); (United States)},
issn = {0556-2821},
number = ,
volume = 51:4,
place = {United States},
year = {1995},
month = {2}
}