Gluon condensate in charmonium sum rules with 3-loop corrections
Abstract
Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of dimension 4 gluon condensate. The moments M_n(Q^2) of the polarization operator of vector charm currents are calculated and compared with experimental data. The 3-loop (alpha_s^2) perturbative corrections, the gluon condensate contribution with alpha_s corrections and dimension 6 operator G^3 contribution 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 G^3 contribution is large. The domain in the plane (n, Q^2), where the sum rules are legitimate, is found. Strong correlation of the values of gluon condensate and MS-bar charm quark mass quark is determined. The absolute limits are found to be for gluon condensate <(alpha_s/pi)G^2>=0.009+-0.007 GeV^4 and for charm quark mass m(m)=1.275+-0.015 GeV in MS-bar scheme.
Keywords
Cite
@article{arxiv.hep-ph/0207183,
title = {Gluon condensate in charmonium sum rules with 3-loop corrections},
author = {B. L. Ioffe and K. N. Zyablyuk},
journal= {arXiv preprint arXiv:hep-ph/0207183},
year = {2011}
}
Comments
23 pages, 1 latex + 9 eps files. v2: additions to sections 2 and 8, conclusion unchanged; to be published in EPJC