Aspects of the Confinement Mechanism in Coulomb-Gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in the Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.

Figure 1

The pion and rho masses as functions of the current-quark mass in the limit ${\mu }_{\mathrm{IR}}\to 0$. All quantities are given in appropriate units of $\sqrt{{\sigma }_c}$, ${\sigma }_c$ being the Coulomb string tension (see text).

Figure 2

The quark mass function $M(q^2)$ for four values of the infrared regulator ${\mu }_{\mathrm{IR}}$ in the chiral limit $m=0$. All quantities are given in appropriate units of $\sqrt{{\sigma }_c}$.

Figure 3

The masses of the $\rho$ as well as the scalar (SD) and axial-vector (AD) diquarks as functions of the infrared regulator ${\mu }_{\mathrm{IR}}$ in the chiral limit. The mass of the $\pi$ is identically zero for all values of ${\mu }_{\mathrm{IR}}$ and therefore not shown in the graph. All quantities are given in appropriate units of $\sqrt{{\sigma }_c}$.

Figure 4

Pion Bethe-Salpeter amplitude components $g$ and $h$ as functions of the infrared regulator ${\mu }_{\mathrm{IR}}$. For convenience, the amplitudes are normalized such that $h(0)=1$. All quantities are given in appropriate units of $\sqrt{{\sigma }_c}$.

Figure 5

Same as Fig. 4 for the scalar diquark.

Figure 6

Charge radii for $\pi$ meson as well as SD as functions of the infrared regulator ${\mu }_{\mathrm{IR}}$. All quantities are given in appropriate units of $\sqrt{{\sigma }_c}$.