A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context

Abstract

In this paper 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 $q\overline{q}$ case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the $3q$ case we find a spin dependent potential identical to that already derived in the literature from the ad hoc and non correct assumption of scalar confinement. Furthermore we obtain the correct form of the spin independent potential up to the $1/m^2$ order.

30 pages, Revtex (3 figures available as hard copies only), IFUM 452/FT

Cited by in corpus (68)

• 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
• 50 Years of Quantum Chromodynamics
• Effective Field Theory Lagrangians for Baryons with Two and Three Heavy Quarks
• The QCD Potential at $O(1/m)$
• On the running coupling constant in QCD
• Ground-state triply and doubly heavy baryons in a relativistic three-quark model
• The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result
• Matching at one loop for the four-quark operators in NRQCD
• A lattice determination of QCD field strength correlators
• On the Dirac Structure of Confinement
• Infrared behavior of the running coupling constant and bound states in QCD
• A first estimate of triply heavy baryon masses from the pNRQCD perturbative static potential
• Quark-antiquark potential with retardation and radiative contributions and the heavy quarkonium mass spectra
• Heavy Quarkonia: Wilson Area Law, Stochastic Vacuum Model and Dual QCD
• Charm and Bottom Baryon Decays in the Bethe-Salpeter Approach: Heavy to Heavy Semileptonic Transitions
• Confinement: Understanding the Relation Between the Wilson Loop and Dual Theories of Long Distance Yang Mills Theory
• The three-quark static potential in perturbation theory
• Interpretation of $D_{sJ}(2632{)}^{+}$, $D_{s1}(2700{)}^{\pm }$, $D_{sJ}^{\star }(2860{)}^{+}$ and $D_{sJ}(3040{)}^{+}$
• From Current to Constituent Quarks: a Renormalization Group Improved Hamiltonian-based Description of Hadrons
• Non-perturbative dynamics of the heavy-light quark system in the non-recoil limit
• One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium
• Poincare' invariance and the heavy-quark potential
• Effective string theory and the long-range relativistic corrections to the quark-antiquark potential
• Testing confining potentials through meson/baryon hyperfine splitting ratio
• Bound state equation in the Wilson loop approach with minimal surfaces
• Three-body relativistic flux tube model from QCD Wilson-loop approach
• Bethe--Salpeter equation in QCD
• Baryon Magnetic Moments in a QCD-based Quark Model with loop corrections
• Nonperturbative evaluation of a field correlator appearing in the heavy quarkonium system
• Glueball phenomenology and the relativistic flux tube model
• Variational Minimization on String-rearrangement Surfaces, Illustrated by an Analysis of the Bilinear Interpolation
• Fermion Confinement by a Relativistic Flux Tube
• Pure bosonic worldline path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD
• Effective field theory and the quark model
• From the Feynman-Schwinger representation to the non-perturbative relativistic bound state interaction
• Vector and scalar confinement in gauge theory with a dilaton
• From scalar to string confinement
• Spin-dependent forces of quarks in baryon
• Two- and three-body color flux tubes in the Chromo Dielectric Model
• Renormalization approach to constituent quark models of Quarkonium
• Effective field theory and the quark model, II. Structure of loop corrections
• Adiabatic string shape for non-uniform rotation
• Effective potential between two gluons from the scalar glueball
• Bound state equivalent potentials with the Lagrange mesh method
• Analysis of dynamical corrections to baryon magnetic moments
• Integral equation for gauge invariant quark two-point Green's function in QCD
• Relativistic corrections for two- and three-body flux tube model
• Models and Potentials in Hadron Spectroscopy
• Electromagnetic corrections to baryon masses
• Pressure and interaction measure of the gluon plasma
• f [N pi N]: from quarks to the pion derivative coupling
• Quarkonium Spectroscopy: Beyond One-Gluon Exchange
• Baryon masses in a loop expansion with form factor
• Spin-String Interaction in QCD Strings
• String junction as a baryonic constituent
• Estimates of isospin breaking contributions to baryon masses
• A parametrization of the baryon octet and decuplet masses
• Gauge invariant bound state equations for quark-antiquark systems in QCD
• The Impact of NLO-Corrections on the Determination of the $\bar{u},\bar{d} Content of Nucleons from Drell-Yan Production
• The minimum area, the flux tube, and Thomas precession
• Potential models, sum rules, color singlet model versus NREFT in Heavy Quarkonium
• Gluelump spectrum from Coulomb gauge QCD
• Two-point gauge invariant quark Green's functions with polygonal phase factor lines
• Gauge-invariant approach to quark dynamics
• Flux Tubes in Effective Field Theory