2020 Impact factor 4.590
Particles and Fields
Eur. Phys. J. C 27, 229-241 (2003)
DOI: 10.1140/epjc/s2002-01099-8

Gluon condensate in charmonium sum rules with three-loop corrections

B.L. Ioffe and K.N. Zyablyuk

Institute of Theoretical and Experimental Physics, B.Cheremushkinskaya 25, Moscow 117218, Russia

(Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 )

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.

© Società Italiana di Fisica, Springer-Verlag 2003