  It is conventional to choose a typical momentum transfer of the process as
the renormalization scale and take an arbitrary range to estimate the
uncertainty in the QCD prediction. However, predictions using this procedure
depend on the renormalization scheme, leave a non-convergent renormalon
perturbative series, and moreover, one obtains incorrect results when applied
to QED processes. In contrast, if one fixes the renormalization scale using the
Principle of Maximum Conformality (PMC), all non-conformal $\{\beta_i\}$-terms
in the perturbative expansion series are summed into the running coupling, and
one obtains a unique, scale-fixed, scheme-independent prediction at any finite
order. The PMC scale $\mu^{\rm PMC}_R$ and the resulting finite-order PMC
prediction are both to high accuracy independent of the choice of initial
renormalization scale $\mu^{\rm init}_R$, consistent with renormalization group
invariance. As an application, we apply the PMC procedure to obtain NNLO
predictions for the $t\bar{t}$-pair production at the Tevatron and LHC
colliders. The PMC prediction for the total cross-section $\sigma_{t\bar{t}}$
agrees well with the present Tevatron and LHC data. We also verify that the
initial scale-independence of the PMC prediction is satisfied to high accuracy
at the NNLO level: the total cross-section remains almost unchanged even when
taking very disparate initial scales $\mu^{\rm init}_R$ equal to $m_t$,
$20\,m_t$, $\sqrt{s}$. Moreover, after PMC scale setting, we obtain
$A_{FB}^{t\bar{t}} \simeq 12.5%$, $A_{FB}^{p\bar{p}} \simeq 8.28%$ and
$A_{FB}^{t\bar{t}}(M_{t\bar{t}}>450 \;{\rm GeV}) \simeq 35.0%$. These
predictions have a $1\,\sigma$-deviation from the present CDF and D0
measurements; the large discrepancy of the top quark forward-backward asymmetry
between the Standard Model estimate and the data are thus greatly reduced.
