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Lattice gluon and ghost propagators and the strong coupling in pure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects

2016; American Physical Society; Volume: 94; Issue: 1 Linguagem: Inglês

10.1103/physrevd.94.014502

2470-0037

Anthony G. Duarte, Orlando Oliveira, Paulo J. Silva,

High-Energy Particle Collisions Research

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 $\ensuremath{\sim}(13\text{ }\text{ }\mathrm{fm}{)}^{4}$ and $\ensuremath{\sim}(8\text{ }\text{ }\mathrm{fm}{)}^{4}$, 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 ${\ensuremath{\alpha}}_{s}({p}^{2})$, 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 $\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$.