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Gluon condensate in charmonium sum rules with three-loop corrections

  • B.L. Ioffe
  • K.N. Zyablyuk
Theoretical Physics

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 M n (Q 2 ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop (\(\alpha_{\mathrm{s}}^2\)) 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 Q 2 = 0, where the perturbation series diverges and the G3 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 \(\overline{\mathrm{MS}}\) 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.

Keywords

Experimental Data Strong Correlation Quark Mass Polarization Operator Charm Quark 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg / Società Italiana di Fisica 2003

Authors and Affiliations

  • B.L. Ioffe
    • 1
  • K.N. Zyablyuk
    • 1
  1. 1.Institute of Theoretical and Experimental Physics, B.Cheremushkinskaya 25, Moscow 117218, Russia RU

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