Quark Schwinger-Dyson Evaluation of the l1, l2 Coefficients in the Chiral Lagrangian

Abstract

Using a systematic expansion of the quark-antiquark Bethe-Salpeter wavefunctions in the relativistic quark model and working to O(P^4), 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.