Gluon condensate in charmonium sum rules with three-loop correctionsB.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 ( ) perturbative corrections, the contribution of the gluon condensate with 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 charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme.
© Società Italiana di Fisica, Springer-Verlag 2003