Quark Schwinger-Dyson evaluation of thel1,l2coefficients in the chiral Lagrangian

Abstract

Using a systematic expansion of the quark-antiquark Bethe-Salpeter wave functions 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 ${l}_{1}{,l}_{2}$ to the underlying quark-antiquark wave functions 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.