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We analyze the sigma meson mass and width together with the pion-pionscattering parameters in the context of non-local chiral quark models withwave-function renormalization (WFR). We consider both non-local interactionsbased on the frequently used exponential form factor, and on fits to the massand renormalization functions obtained in lattice calculations. In the case ofthe sigma properties we obtain results which are less dependent on theparameterization than in the standard local NJL model, and which are inreasonable agreement with the recently reported empirical values. We also showthat the inclusion of the WFR tend to improve the description of the $\pi-\pi$scattering parameters, with the lattice inspired parameterization providing thebest overall results. Finally, we analyze the connection of the non-local quarkmodels discussed here with Chiral Perturbation Theory, and present the modelpredictions for the low energy constants relevant for $\pi-\pi$ scattering toO(4) in the chiral expansion.

Nonlocal chiral quark models with wavefunction renormalization: sigma properties and \pi-\pi scattering parameters