DOI: 10.1140/epjc/s2002-01099-8
Gluon condensate in charmonium sum rules with three-loop corrections
B.L. Ioffe and K.N. ZyablyukInstitute 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 )
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 (
) 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
