Heavy Quarkonia: Wilson Area Law, Stochastic Vacuum Model and Dual QCD

Abstract

The $Q\bar{Q}$ semirelativistic interaction in QCD can be simply expressed in terms of the Wilson loop and its functional derivatives. In this approach we present the $Q\bar{Q}$ potential up to order $1/m^2$ using the expressions for the Wilson loop given by the Wilson Minimal Area Law (MAL), the Stochastic Vacuum Model (SVM) and Dual QCD (DQCD). We confirm the original results given in the different frameworks and obtain new contributions. In particular we calculate up to order $1/m^2$ the complete velocity dependent potential in the SVM. This allows us to show that the MAL model is entirely contained in the SVM. We compare and discuss also the SVM and the DQCD potentials. It turns out that in these two very different models the spin-orbit potentials show up the same leading non-perturbative contributions and 1/r corrections in the long-range limit.

29 pages, revtex, 1 figure(fig1.ps); replaced with the last version that will appear in Phys. Rev. D (1March 1997); few misprints corrected

References in corpus (2)

• Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
• Nonperturbative evaluation of a field correlator appearing in the heavy quarkonium system

Cited by in corpus (38)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• QCD forces and heavy quark bound states
• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Mass spectrum of orbitally and radially excited heavy-light mesons in the relativistic quark model
• 50 Years of Quantum Chromodynamics
• Complete O(v^2) corrections to the static interquark potential from SU(3) gauge theory
• The QCD Potential at $O(1/m)$
• The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result
• Spin-dependent potentials from lattice QCD
• Phenomenological prediction of the properties of the B_{C} system
• A lattice determination of QCD field strength correlators
• Self-contained definition of the Collins-Soper kernel
• The $B_c$ mass up to order ${\alpha }_s^4$
• Field Strength Correlators and Dual Effective Dynamics in QCD
• Quark-antiquark potential with retardation and radiative contributions and the heavy quarkonium mass spectra
• Non-perturbative dynamics of the heavy-light quark system in the non-recoil limit
• Poincare' invariance and the heavy-quark potential
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Effective string theory and the long-range relativistic corrections to the quark-antiquark potential
• Spin-dependent interactions in quarkonia
• Comparion of Lattice and Dual QCD Results for Heavy Quark Potentials
• Variational Minimization on String-rearrangement Surfaces, Illustrated by an Analysis of the Bilinear Interpolation
• Relativistic corrections to the static potential at O(1/m) and O(1/m^2)
• Pure bosonic worldline path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD
• Potential regime for heavy quarks dynamics and Lorentz nature of confinement
• From the Feynman-Schwinger representation to the non-perturbative relativistic bound state interaction
• Heavy Hadron Spectroscopy
• Relativistic corrections to the static energy in terms of Wilson loops at weak coupling
• Heavy-quark binding and kinetic energies in heavy-light mesons and the constituent quark model
• Current Topics in Heavy Quarkonium Physics
• Spin-String Interaction in QCD Strings
• The colormagnetic confinement in QCD
• Potential models, sum rules, color singlet model versus NREFT in Heavy Quarkonium
• Flavor independence and the dual superconducting model of QCD
• Nonperturbative QCD Vacuum Effects in Nonlocal Quark Dynamics
• Stochastic vacuum model and dual theory: a comparison in the context of the heavy quarkonia potential