  There a sizable and systematic discrepancy between experimental data on the
$\bar{b}b$ production in $\bar{\mathrm p}$p, $\gamma$p and $\gamma\gamma$
collisions and existing theoretical calculations within perturbative QCD.
Before interpreting this discrepancy as a signal of new physics, it is
important to understand quantitatively the ambiguities of conventional
calculations. In this paper the uncertainty coming from renormalization and
factorization scale dependence of finite order perturbation calculations of the
total cross section of $\bar{b}b$ production in $\bar{\mathrm{p}}$p collisions
is discussed in detail. It is shown that the mentioned discrepancy is reduced
significantly if these scales are fixed via the Principle of Minimal
Sensitivity.
