Infrared gluon propagator from lattice QCD: Results from large asymmetric lattices

The infrared limit of the lattice Landau gauge gluon propagator is studied. We show that the lattice data are compatible with the pure power law $(q^2{)}^{2\kappa }$ solution of the Dyson-Schwinger equations. Using various lattice volumes, the infinite volume limit for the exponent $\kappa$ is measured. Although, the results allow $\kappa =0.498–0.525$, the lattice data favor $\kappa \sim 0.52$, which would imply a vanishing zero momentum gluon propagator.

Figure 1

Bare gluon dressing function for all momenta for the largest (top) and the two smallest (bottom) lattices. The figure shows the gluon propagator computed with pure temporal momenta $q_t$ and pure spatial momenta $q_x$. For the spatial momenta a $Z_3$ average was performed.

Figure 2

Bare gluon dressing function for temporal momenta for all lattices volumes. For comparisation, the figure includes the ${16}^3\times 48$ and ${32}^3\times 64$ propagators computed at $\beta =6.0$ in 26.

Figure 3

$\kappa$ as a function of the inverse volume. Note that in order to make the plot more clear, the $\kappa$ from the fits to the corrections to the pure power law were shifted in the $1/V$ axis.

Figure 4

Bare gluon propagator for the two smallest momenta as a function of the inverse volume. For comparison, for zero momentum we include $D(0)$ from the largest lattice of 26, i.e. ${32}^3\times 64$.

Figure 5

Bare gluon propagator as a function of the inverse volume for the third and fourth smallest momenta.

Figure 6

The bare extrapolated gluon propagator. The full range of temporal momenta is seen on the top with a zoom for the infrared region on the bottom. The errors on the propagator were computed assuming a Gaussian error propagation. For comparison, the figure includes the ${16}^3\times 48$ and ${32}^3\times 64$ propagators computed at $\beta =6.0$ in 26.