Analytic structure of the Landau gauge quark propagator from Padé analysis

Abstract

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Pad\'e approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e., for a Minkowski type of momentum. This pole occurs at Euclidean momenta $p\ensuremath{\sim}\ensuremath{-}300\text{ }\text{ }\mathrm{MeV}$ and it reproduces typical quark mass values used in phenomenological effective quark models. The Pad\'e approximant analysis also gives hints on the presence of a branch cut. Our results also show a clear correlation between the position of this pole, understood as an effective quark mass, and the pion mass that is compatible with partial conservation of the axial current. Slightly differences between the poles for the two quark form factors are observed which can be viewed either as a limitation of the method or as a suggestion that the quark propagator has no spectral representation.