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Next to leading order corrections to the $SU(3) \times SU(3)$Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD FiniteEnergy Sum Rules (FESR) involving the pseudoscalar current correlator. Twotypes of integration kernels in the FESR are used to suppress the contributionof the kaon radial excitations to the hadronic spectral function, one withlocal and the other with global constraints. The result for the pseudoscalarcurrent correlator at zero momentum is $\psi_5(0) = (2.8 \pm 0.3) \times10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55\pm 5)%$. The resulting uncertainties are mostly due to variations in the upperlimit of integration in the FESR, within the stability regions, and to a muchlesser extent due to the uncertainties in the strong coupling and the strangequark mass. Higher order quark mass corrections, vacuum condensates, and thehadronic resonance sector play a negligible role in this determination. Theseresults confirm an independent determination from chiral perturbation theorygiving also very large corrections, i.e. roughly an order of magnitude largerthan the corresponding corrections in chiral $SU(2) \times SU(2)$. Combiningthese results with our previous determination of the corrections to GMOR inchiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two lowenergy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3)\times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at thescale of the $\rho$-meson mass.

Corrections to the ${\bf SU(3)\times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$