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.

• Received 17 June 2003

DOI:https://doi.org/10.1103/PhysRevD.68.094014