Stanley J. Brodsky, Xing-Gang Wu
The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. 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 choice of renormalization scheme, 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 renormalization scale $\mu^{\rm PMC}_R$ and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale $\mu^{\rm init}_R$. As an application, we apply the PMC procedure to obtain NNLO predictions for the $t\bar{t}$-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for $\sigma_{t\bar{t}}$ is larger in magnitude in comparison with the conventional scale-setting method, and it 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 $m_t$, $20\,m_t$, $\sqrt{s}$.
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http://arxiv.org/abs/1203.5312
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