CHIRAL SUM-RULES TO 2ND-ORDER IN QUARK MASS

A new calculation of the isospin and hypercharge axial-vector current propagators [Delta(A33)(mu nu)(q(2)) and Delta(A88)(mu nu)(q(2))] to t wo loops in SU(3) X SU(3) chiral perturbation theory is used to derive chiral spectral function sum rules valid to second order in the light quark masses. Explicit farms are given for the three-pion isospin axi al-vector spectral functions at low energy, and application of the sum rules to the determination of counterterms of the chiral Lagrangian i s discussed.