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The problem of renormalization scheme dependence in QCD
perturbation theory remains on obstacle to mak- ing precise tests
of the theory. The renormalization scale dependence of
dimensionless physical QCD observable, depending on a single
energy scale $Q$, can be avoided provided that all ultraviolet
logarithms which build the physical energy dependence on $Q$ are
resummed. This was termed complete Renormalization Group improve-
ment(CORGI). This argument can be extended to processes involving
factorization of operator matrix elements and coefficient
functions. We are trying to employ the idea of CORGI approach on
analyzing of heavy quarks production in hadron collisions. There
is a sizable and systematic discrepancy between experimental data
on the $b\overline{b}$ production in $p\overline{p}$, $\gamma p$
and $\gamma \gamma$ collisions and existing theoretical
calculations within perturbative QCD. One suggested way to cope
with this discrepancy is to employ the CORGI approach in which one
should perform a resummation to all-orders of renormalization and
factorization group -predictable terms at each order of pertur-
bation theory. Then the scales dependence will be avoided and it
is expected that the mentioned discrepancy is reduced
signi�cantly.
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