Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M-n (Q(2)) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop (alpha(S)(2)) perturbative corrections, the contribution of the gluon condensate with alpha(s) corrections and the contribution of the dimension 6 operator G(3) are accounted. It is shown that the sum rules for the moments do not work at Q(2) = 0, where the perturbation series diverges and the G(3) contribution is large. The domain in the (n, Q(2)) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and (MS) over bar charm quark mass is determined. The absolute limits are found to be for the gluon condensate <(alpha(s)/pi)G(2))> = 0.009 +/- 0.007 GeV4 < for the charm quark mass (m) over bar((m) over bar) = 1.275 +/- 0.015 GeV in the (MS) over bar scheme.