Gluon condensate in charmonium sum rules with three-loop corrections

By B. Ioffe, K. Zyablyuk. 2002

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Abstract. Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments Mn(Q2) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop ($\alpha_{\mathrm{s}}^2$) perturbative corrections, the contribution of the gluon condensate with $\alpha_{\mathrm{s}}$ corrections and the contribution of the dimension 6 operator G3 are accounted. It is shown that the sum rules for the moments do not work at Q2 = 0, where the perturbation series diverges and the G3 contribution is large. The domain in the (n, Q2) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and $\overline{\mathrm{MS}}$ charm quark mass is determined. The absolute limits are found to be for the gluon condensate $\langle ({\alpha_{\mathrm{s}}} /{\pi}) G^2 \rangle = 0.009\pm 0.007{\mathrm{GeV}}^4$ and for the charm quark mass ${\bar m}({\bar m}) = 1.275\pm 0.015 {\mathrm{GeV}}$ in the $\overline{\mathrm{MS}}$ scheme.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/2ed2154f915c3ced93751f2cc6dbd502df5f4c02