Chiral Meson Lagrangians from the QCD Based NJL Model Modified by Nonlocal Effects

Starting from a QCD inspired bilocal quark interaction we obtain a local effective meson lagrangian. In contrast to previous local (NJL-like) approaches, we include nonlocal corrections related to the finite meson size which we characterize by a small parameter. After bosonization using the heat-kernel method we predict the structure coefficients of the Gasser-Leutwyler $p^4$-lagrangian up to first order in this parameter. The modifications for the $L_i$ coefficients are typically of the order 10-20\%, except for $L_5$, where we find a stronger nonlocal influence.