We analyze the sigma meson mass and width together with the pion-pion scattering parameters in the context of nonlocal chiral quark models with wave function renormalization (WFR). We consider both nonlocal interactions based on the frequently used exponential form factor, and on fits to the quark mass and renormalization functions obtained in lattice calculations. In the case of the sigma properties, we obtain results which are less dependent on the parametrization than in the standard local Nambu-JonaLasinio model, and which are in reasonable agreement with the recently reported empirical values. We also show that the inclusion of the WFR tend to improve the description of the -scattering parameters, with the lattice inspired parametrization providing the best overall results. Finally, we analyze the connection of the nonlocal quark models discussed here with chiral perturbation theory, and present the model predictions for the low-energy constants relevant for -scattering to Oð4Þ in the chiral expansion.

We define the pion-photon transition distribution amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu-Jona-Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and the polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.

Recent BaBaR data on the pion transition form factor, whose Q 2 dependence is much steeper then predicted by asymptotic Quantum Chromodynamics (QCD), have caused a renewed interest in its theoretical description. We present here a formalism based on a model independent low energy description and a high energy description based on QCD, which match at a scale Q0. The high energy description incorporates a flat pion distribution amplitude, φ (x) = 1, at the matching scale Q0 and QCD evolution from Q0 to Q > Q0. The flat pion distribution is connected, through soft pion theorems and chiral symmetry, to the pion valance parton distribution at the same low scale Q0. The procedure leads to a good description of the data, and incorporating additional twist three effects, to an excellent description of the data.