Chiral sum rules to second order in quark mass

Abstract

A new calculation of the isospin and hypercharge axialvector current propagators (${\Delta }_{A33}^{\mu \nu }(q^2)$ and ${\Delta }_{A88}^{\mu \nu }(q^2)$) 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.

Comments: Figures extended down to threshold; Eq. (19) expressed in simplified form