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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 nonconvergent 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 nonconformal {₈} 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 ₑ^PMC and the resulting finite-order PMC prediction are both to high accuracy independent of the choice of initial renormalization scale ₑ^init, consistent with renormalization group invariance. As an application, we apply the PMC procedure to obtain next-to-next-to-leading-order (NNLO) predictions for the tt-pair production at the Tevatron and LHC colliders. The PMC prediction for the total cross section ₓₓ 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 ₑ^init equal to mₓ, 20mₓ, and s. Moreover, after PMC scale setting, we obtain A₅₁^tt12. 5%, A₅₁^pp8. 28% and A₅₁^tt (Mₓₓ>450 GeV) 35. 0%. These predictions have a 1 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.
Brodsky et al. (Mon,) studied this question.