Corrections to the SU ( 3 ) × SU ( 3 ) Gell - Mann - Oakes - Renner

Next to leading order corrections to the SU(3) × SU(3) Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is ψ5(0) = (2.8± 0.3)× 10−3 GeV, leading to the chiral corrections to GMOR: δK = (55 ± 5)%. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral SU(2) × SU(2). Combining these results with our previous determination of the corrections to GMOR in chiral SU(2) × SU(2), δπ, we are able to determine two low energy constants of chiral perturbation theory, i.e. L8 = (1.0 ± 0.3) × 10−3, and H 2 = −(4.7 ± 0.6) × 10−3, both at the scale of the ρ-meson mass. ∗Supported in part by MEC and FEDER (EC) under grant FPA2011-23596 and GV under grant PROMETEO2010-056 and BEST12, by NRF (South Africa), and by the Alexander von Humboldt Foundation (Germany).