Gluon propagator with two-loop Schwinger-Dyson equations

Gluon, ghost, and quark propagators are computed in the Schwinger-Dyson formalism. The full set of one-loop and two-loop contributions to the gap equations are evaluated for the first time. A new and efficient method for dealing with quadratic divergences is presented and a consistent renormalization method is proposed. We find that the two-loop contribution to the propagators is subleading, good fits to lattice data are possible, and reliable vertex models are important to obtaining desired ultraviolet, infrared, and gauge-symmetric behavior.

Figure 1

Quark and ghost gap equations. Crosses represent bare quantities.

Figure 2

Gluon propagator Schwinger-Dyson equation. The last two diagrams are the sunset and squint diagrams, respectively.

Figure 3

The quark wave function renormalization, $Z_q=1/A$, and dynamical quark mass, $M$, along with lattice results [21].

Figure 4

Ghost dressing function and the lattice data [19].

Figure 5

Gluon dressing function and the lattice data [19].

Figure 6

Quenched data (solid points); quenched SDE (solid line); $n_f=3$ lattice (open points); and unquenched SDE ($n_f=3$, dashed line). Data are from [20].

Figure 7

Quenched data (solid points); quenched SDE (solid line); $n_f=3$ lattice (open points); and unquenched SDE (dashed line). Data are from [20]. The simple three-gluon vertex model is with $G(0.5\mathrm{GeV},n_f=0)=7.5{\mathrm{GeV}}^{-2}$, $G(0.5\mathrm{GeV},n_f=3)=6.0{\mathrm{GeV}}^{-2}$, and $g_q=0.57$.

Figure 8

Total (solid line), two-gluon (dashed), quark (small dash), ghost (dotted), sunset (dash-dot), and squint (long dash-dot) polarization functions.