Gluon condensate and c-quark mass in pseudoscalar sum rules at 3-loop order

Abstract

Charmonium sum rules for pseudoscalar 0^{-+} state eta_c(1S) are analyzed within perturbative QCD and Operator Product Expansion. The perturbative part of the pseudoscalar correlator is considered at alpha_s^2 order and the contribution of the gluon condensate <G^2> is taken into account with alpha_s correction. The OPE series includes the operators of dimension D=6,8 computed both in the instanton and factorization model. The method of moments in MS-bar scheme allows to establish acceptable values of the charm quark mass and gluon condensate, using the experimental mass of eta_c. In result of the analisys the charm quark mass is found to be m_c(m_c)=1.26+-0.02 GeV independently of the condensate value. The sensitivity of the results to various approximations for the massive 3-loop pseudoscalar correlator is discussed.