Mesons and diquarks in Coulomb-gauge QCD

I demonstrate how confinement in Coulomb-gauge QCD makes quark-quark states of the color anti-triplet (diquarks) move out of the physical spectrum. Mesons as color singlet quark-antiquark states, on the other hand have finite masses and for highly excited states in the meson spectra effective restoration of chiral symmetry can be observed. In Coulomb-gauge QCD the 00-component of the gluon propagator Dμν(~x, t) has an instantaneous part VC(~x)δ(t) and confinement means that −VC(~x)→∞ for |~x| → ∞. It was shown that Coulomb confinement is a necessary condition for confinement, i.e., that the gauge invariant quark-antiquark potential VW (r) goes to infinity for r → ∞ [1]. An almost linearly rising Coulomb potential has been suggested [2], which was also confirmed by results from the lattice [3]. In momentum space it becomes VC(|~k|) = σC |~k|4 , (1) where σC is the Coulomb string tension. Based on previous works [4] we performed a study of the mechanism of Coulomb confinement in the Dyson-Schwinger–Bethe-Salpeter framework [5] in Rainbow-ladder approximation [6]. We took into account only the Coulomb potential (1) and neglected transverse gluons and noninstantaneous contributions to D00. In that way all integrals over k0 can be performed analytically and one has to deal with three-dimensional integral equations only. (1) has also an unrealistic ultraviolet (UV) behavior. However, it has the advantage that it produces no UV divergences, thus making renormalization not necessary. Due to all these approximations some physics is lost and the model is not expected to provide realistic quantitative results but some qualitative insight into the physics of confinement in QCD. Since the axial-vector Ward-Takahashi