Quark sector of the QCD groundstate in Coulomb gauge

Abstract

The variational approach to Yang-Mills theory in Coulomb gauge is extended to full QCD. For the quark sector we use a trial wave functional, which goes beyond the previously used BCS-type state and which explicitly contains the coupling of the quarks to transverse gluons. This quark wave functional contains two variational kernels: one is related to the quark condensate and occurs already in the BCS-type states; the other represents the form factor of the coupling of the quarks to the transverse gluons. Minimization of the energy density with respect to these kernels results in two coupled integral (gap) equations. These equations are solved numerically using the confining part of the non-Abelian color Coulomb potential and the lattice static gluon propagator as input. With the additional coupling of quarks to transverse gluons included, the low energy chiral properties increase substantially towards their phenomenological values. We obtain a reasonable description of the chiral condensate, which for a vanishing current quark mass is obtained in the range of 190--235 MeV. The coupling of the quarks to the transverse gluons enhances the constituent quark mass by about 60% in comparison to the pure BCS Ansatz.