Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects

The dependence of the Landau gauge two point gluon and ghost correlation functions on the lattice spacing and on the physical volume are investigated for pure SU(3) Yang-Mills theory in four dimensions using lattice simulations. We present data from very large lattices up to ${128}^4$ and for two lattice spacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\sim$ (13 fm)${}^4$ and $\sim$ (8 fm)${}^4$, respectively. Our results show that, for sufficiently large physical volumes, both propagators have a mild dependence on the lattice volume. On the other hand, the gluon and ghost propagators change with the lattice spacing $a$ in the infrared region, with the gluon propagator having a stronger dependence on $a$ compared to the ghost propagator. In what concerns the strong coupling constant ${\alpha }_s(p^2)$, as defined from gluon and ghost two point functions, the simulations show a sizeable dependence on the lattice spacing for the infrared region and for momenta up to $\sim 1$ GeV.