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

Abstract

The next to leading order chiral corrections to the S U ( 2 ) × S U ( 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, δ π , the value δ π = ( 6.2 ± 1.6 ) % . As a byproduct, the chiral perturbation theory (unphysical) low energy constant H 2 r is determined to be H 2 r ( ν χ = M ρ ) = − ( 5.1 ± 1.8 ) × 10 − 3 .