Revised variational approach to QCD in Coulomb gauge

Abstract

The variational approach to QCD in Coulomb gauge is revisited. By assuming the non-Abelian Coulomb potential to be given by the sum of its infrared and ultraviolet parts, i.e.~by a linearly rising potential and an ordinary Coulomb potential, and by using a Slater determinant ansatz for the quark wave functional, which contains the coupling of the quarks and the gluons with two different Dirac structures, we obtain variational equations for the kernels of the fermionic vacuum wave functional, which are free of ultraviolet divergences. Thereby, a Gaussian type wave functional is assumed for the gluonic part of the vacuum. By using the results of the pure Yang--Mills sector for the gluon propagator as input, we solve the equations for the fermionic kernels numerically and calculate the quark condensate and the effective quark mass in leading order. Assuming a value of ${\sigma }_{\mathrm{C}}=2.5\sigma$ for the Coulomb string tension (where $\sigma$ is the usual Wilsonian string tension) the phenomenological value of the quark condensate $⟨\bar{\psi }\psi ⟩\simeq (-235\mathrm{MeV}{)}^3$ is reproduced with a value of $g\simeq 2.1$ for the strong coupling constant of the quark-gluon vertex.

References in corpus (15)

• Coulomb Gauge QCD, Confinement, and the Constituent Representation
• Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
• On the Yang-Mills wave functional in Coulomb gauge
• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Coulomb gauge gluon propagator and the Gribov formula
• $\bar{q}q$ condensate for light quarks beyond the chiral limit
• Leading order infrared quantum chromodynamics in Coulomb gauge
• The effective Coulomb potential in SU(3) lattice Yang-Mills theory
• Chiral symmetry breaking in Hamiltonian QCD in Coulomb gauge
• Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
• Coulomb vs. physical string tension on the lattice
• Quark Sector of the QCD Groundstate in Coulomb Gauge
• Improved variational approach to QCD in Coulomb gauge
• Scaling study of the gluon propagator in Coulomb gauge QCD on isotropic and anisotropic lattices
• Coulomb string tension, asymptotic string tension, and the gluon chain

Cited by in corpus (13)

• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Correlation functions of Landau gauge Yang-Mills theory
• Infrared massive gluon propagator from a BRST-invariant Gribov horizon in a family of covariant gauges
• Chiral symmetry restoration at finite temperature within the Hamiltonian approach to QCD in Coulomb gauge
• Three-point vertex functions in Yang-Mills Theory and QCD in Landau gauge
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Variational and Dyson--Schwinger Equations of Hamiltonian Quantum Chromodynamics
• An exploratory study of Yang-Mills three-point functions at non-zero temperature
• The Equal-Time Quark Propagator in Coulomb Gauge
• Dynamical Quark Mass Generation in QCD\textsubscript{3} within the Hamiltonian approach in Coulomb gauge
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• Dyson--Schwinger Approach to Hamiltonian QCD