Chiral Corrections to the Gell-Mann-Oakes-Renner Relation from QCD Sum Rules

Abstract

We calculate the next-to-leading order corrections to the $SU(2)\otimes SU(2)$ and $SU(3)\otimes SU(3)$ Gell-Mann-Oakes-Renner relations. We use a pseudoscalar correlator calculated from Perturbative QCD up to five loops and use the QCD Finite Energy Sum Rules with integration kernels tuned to suppress the importance of the hadronic resonances. This leads to a substantial reduction in the systematic uncertainties from the experimentally unknown resonance spectral function. We use the method of Fixed Order and Fixed Renormalization Scale Perturbation Theory to compute the integrals. We calculate these corrections to be $\delta_\pi = 0.060 \pm 0.014$ and $\delta _K =0.64 \pm 0.24$. As a result of these new values, we predict the value of the light quark condensate $\left\langle {0|\bar qq|0} \right\rangle = - \left( {266 \pm 5{\text{ MeV}}} \right)^3$ and the Chiral Perturbation Theory low energy constant $H_2^r = - \left( {4.9 \pm 1.8} \right) \times 10^{ - 3}$. Results from this work have been published as: J. Bordes, C.A. Dominguez, P. Moodley, J. Pe$\widetilde{\text{n}}$arrocha and K. Schilcher, J. High Ener. Phys. 05 (2010) 064.