  Next to leading order corrections to the $SU(3) \times SU(3)$
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 $\psi_5(0) = (2.8 \pm 0.3) \times
10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $\delta_K = (55
\pm 5)%$. The resulting uncertainties are mostly due to variations in the 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 $SU(2) \times SU(2)$. Combining
these results with our previous determination of the corrections to GMOR in
chiral $SU(2) \times SU(2)$, $\delta_\pi$, we are able to determine two low
energy 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 the
scale of the $\rho$-meson mass.
