What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices

Abstract

Several analytic approaches predict for SU(N_c) Yang-Mills theories in Landau gauge an enhanced ghost propagator G(p^2) and a suppressed gluon propagator D(p^2) at small momenta. This prediction applies to two, three and four space-time dimensions. Moreover, the gluon propagator is predicted to be null at p = 0. Numerical studies by several groups indeed support an enhanced ghost propagator when compared to the tree-level behavior $1/p^2$ and a finite infrared gluon propagator. However, the agreement between analytic and numerical studies is only at the qualitative level in three and in four dimensions. In particular, the infrared exponent of the ghost propagator seems to be smaller than the one predicted analytically and the gluon propagator seems to display a (finite) nonzero value at zero momentum. It has been argued that this discrepancy might go away once simulations are done on much larger lattice sizes than the ones used up to now. Here we present data in three and four space-time dimensions using huge lattices in the scaling region, i.e. up to 320^3 at beta = 3.0 and up to 128^4 at beta = 2.2, corresponding to V \approx (85 fm)^3 and V \approx (27 fm)^4. Simulations have been done on the IBM supercomputer at the University of Sao Paulo