Spin zero glueballs in the Bethe-Salpeter formalism

The Schwinger-Dyson Bethe-Salpeter approach to the bound state problem is applied to the spin zero glueball spectrum. Although a moderately successful description of the two-point functions and the glueball spectrum can be obtained, further work is required to reduce sensitivity to model truncations.

Figure 1

Quark and ghost gap equations.

Figure 2

Gluon propagator Schwinger-Dyson equation. Solid circles represent full propagators. The open circles represent the full vertex.

Figure 3

Lattice results [16] for the Landau gauge gluon propagator and model fits. Error bars are smaller than the points. Dashed line Eq. (18); dotted line Eq. (19).

Figure 4

The renormalized ghost dressing function and lattice results [16]. Error bars are smaller than the data points. Dashed line, bare vertex model; dotted line, full vertex model.

Figure 5

The quark wave function renormalization, $Z$, and quark running mass, $B$, along with lattice results [17].

Figure 6

Gluonic Bethe-Salpeter equation. Dots represent full propagators and model vertices. Crossed diagrams are not shown.

Figure 7

Ghost Bethe-Salpeter equation.

Figure 8

Quark Bethe-Salpeter equation.

Figure 9

Iterated Bethe-Salpeter equation indicating the BS kernel in the pure gauge case.

Figure 10

Glueball Bethe-Salpeter eigenvalues. Lattice data [22] are represented by the horizontal bars. Solid lines, ground states; dotted lines, first excited states [$\mu =1\mathrm{GeV}$, $g(\mu )=0.41$, intermediate vertex model.]