Two-loop analysis of axial vector current propagators in chiral perturbation theory

We perform a calculation of the isospin and hypercharge axial vector current propagators [${\Delta }_{\mathrm{A}3}^{\mu \nu }\mathrm{}\left(q\right)\mathrm{}$ and ${\Delta }_{\mathrm{A}8}^{\mu \nu }\mathrm{}\left(q\right)\mathrm{}$] to two loops in $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ chiral perturbation theory. A large number of $\mathcal{O}{(p}^6)$ divergent counterterms are fixed, and complete two-loop renormalized expressions for the pion and eta masses and decay constants are obtained. The calculated isospin and hypercharge axial vector polarization functions are used as input in new chiral sum rules, valid to second order in the light quark masses. Some phenomenological implications of these sum rules are considered.