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Title: Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces

Abstract

The quark-antiquark gauge invariant Green function is studied through its dependence on Wilson loops. The latter are saturated, in the large-Nc limit and for large contours, by minimal surfaces. A covariant bound state equation is derived which in the center-of-mass frame and at equal-times takes the form of a Breit-Salpeter type equation. The large-distance interaction potentials reduce in the static case to a confining linear vector potential. In general, the interaction potentials involve contributions having the structure of flux tube like terms.

Authors:
 [1];  [2]
  1. Instituto de Fisica Corpuscular, IFIC, Edificio Institutos de Investigation, Apt. de Correus 22085, E-46071 Valencia (Spain)
  2. Institut de Physique Nucleaire, Groupe de Physique Theorique, Universite Paris XI, F-91406 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
20787644
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 806; Journal Issue: 1; Conference: International workshop on quantum chromodynamics: Theory and experiment, Conversano, Bari (Italy), 16-20 Jun 2005; Other Information: DOI: 10.1063/1.2163769; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; CENTER-OF-MASS SYSTEM; DISTANCE; GAUGE INVARIANCE; GREEN FUNCTION; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARK-ANTIQUARK INTERACTIONS; QUARKS; VECTORS; WILSON LOOP

Citation Formats

Jugeau, F., and Sazdjian, H.. Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces. United States: N. p., 2006. Web. doi:10.1063/1.2163769.
Jugeau, F., & Sazdjian, H.. Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces. United States. doi:10.1063/1.2163769.
Jugeau, F., and Sazdjian, H.. Thu . "Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces". United States. doi:10.1063/1.2163769.
@article{osti_20787644,
title = {Quark-antiquark bound state equation in the Wilson loop approach with minimal surfaces},
author = {Jugeau, F. and Sazdjian, H.},
abstractNote = {The quark-antiquark gauge invariant Green function is studied through its dependence on Wilson loops. The latter are saturated, in the large-Nc limit and for large contours, by minimal surfaces. A covariant bound state equation is derived which in the center-of-mass frame and at equal-times takes the form of a Breit-Salpeter type equation. The large-distance interaction potentials reduce in the static case to a confining linear vector potential. In general, the interaction potentials involve contributions having the structure of flux tube like terms.},
doi = {10.1063/1.2163769},
journal = {AIP Conference Proceedings},
number = 1,
volume = 806,
place = {United States},
year = {Thu Jan 12 00:00:00 EST 2006},
month = {Thu Jan 12 00:00:00 EST 2006}
}
  • We give a new derivation of the quark-antiquark potential in the Wilson loop context. This makes more explicit the approximations involved and enables an immediate extension to the three-quark case. In the [ital q[bar q]] case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the 3[ital q] case we find a spin-dependent potential identical to that already derived in the literature from the [ital ad] [ital hoc] and incorrect assumption of scalar confinement. Furthermore we obtain the correct form of the spin-independent potential up to the 1/[ital m][sup 2] order.
  • The work described in this paper is the first step toward a relativistic three-quark bound-state calculation using a Hamiltonian consistent with the Wigner-Bargmann theorem and macroscopic locality. We give an explicit demonstration that we can solve the two-body problem in momentum space with spin-dependent interactions. The form of the potential is a combination of linear+Coulomb+spin-spin+spin-orbit+tensor, which includes confinement and is of the general form consistent with rotation, space-reflection, and time-reversal invariance. A comparison is made with previous calculations using an alternate technique and with the experimental meson mass spectrum. The results obtained suggest that the model is realistic enough tomore » provide a two-body basis for the three quark baryon problem in which the Poincare group representation is unitary and cluster separability is respected.« less
  • We study the equation of state at finite temperature and density in two-flavor QCD with the renormalization group improved gluon action and the clover-improved Wilson quark action on a 16{sup 3}x4 lattice. Along the lines of constant physics at m{sub PS}/m{sub V}=0.65 and 0.80, we compute the second and forth derivatives of the grand canonical partition function with respect to the quark chemical potential {mu}{sub q}=({mu}{sub u}+{mu}{sub d})/2 and the isospin chemical potential {mu}{sub I}=({mu}{sub u}-{mu}{sub d})/2 at vanishing chemical potentials, and study the behaviors of thermodynamic quantities at finite {mu}{sub q} using these derivatives for the case {mu}{sub I}=0.more » In particular, we study density fluctuations at nonezero temperature and density by calculating the quark number and isospin susceptibilities and their derivatives with respect to {mu}{sub q}. To suppress statistical fluctuations, we also examine new techniques applicable at low densities. We find a large enhancement in the fluctuation of the quark number when the density increased near the pseudocritical temperature, suggesting a critical point at finite {mu}{sub q} terminating the first order transition line between hadronic and quark-gluon-plasma phases. This result agrees with the previous results using staggered-type quark actions qualitatively. Furthermore, we study heavy-quark free energies and Debye screening masses at finite density by measuring the first and second derivatives of these quantities for various color channels of heavy quark-quark and quark-antiquark pairs. The results suggest that, to the leading order of {mu}{sub q}, the interaction between two quarks becomes stronger at finite densities, while that between quark and antiquark becomes weaker.« less