ar X iv : h ep - p h / 03 06 14 6 v 1 17 J un 2 00 3 Quark Schwinger - Dyson Evaluation of the l 1 , l 2 Coefficients in the Chiral Lagrangian

Using a systematic expansion of the quark-antiquark Bethe-Salpeter wavefunctions in the relativistic quark model and working to O(P ), in the chiral limit, we are able to derive theoretical expressions relating the coefficients of the chiral lagrangian l1, l2 to the underlying quark-antiquark wavefunctions and interaction kernels. This is accomplished by using a novel technique based on a Ward Identity for the quark-antiquark ladder kernel which greatly simplifies the required effort. Numerical evaluations are performed in two simple specific models.