Chiral sum rules to second order in quark mass

Abstract

A new calculation of the isospin and hypercharge axialvector current propagators ($Δ_{A33}^{μν}(q^2)$ and $Δ_{A88}^{μν}(q^2)$) to two 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 forms are given for the three-pion isospin axialvector spectral functions at low energy and application of the sum rules to the determination of counterterms of the chiral lagrangian is discussed.