Analytic structure of the Landau gauge quark propagator from Pade acute accent analysis

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Pade ' 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 similar to -300 MeV and it reproduces typical quark mass values used in phenomenological effective quark models. The Pade ' 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.

Automated summary

The analytic structure of two flavorful QCD lattice Landau gauge quark propagators is examined using Pade approximants, which indicate the absence of complex momentum poles for the propagator. However, a real on-axis negative Euclidean momentum pole is observed, indicative of an effective quark mass. This pole is consistent with phenomenological effective quark models and shows a correlation with the pion mass. Slight differences between the poles for the two quark form factors suggest either a limitation of the method or the absence of a spectral representation for the quark propagator.