Gell-Mann-Oakes-Renner Relation: Chiral Corrections from Sum Rules

The next to leading order chiral corrections to the SU(2)×SU(2) Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the light-quark pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. These kernels are designed to suppress hadronic contributions in the region where they are least known. We obtain for the corrections to the GMOR relation, δπ, the value δπ=(6.2±1.6)%. As a byproduct, the chiral perturbation theory (unphysical) low energy constant H2r is determined to be H2r(νχ=Mρ)=−(5.1±1.8)×10−3.