Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality

TL;DR

The PMC procedure is applied to obtain next-to-next- to-leading-order (NNLO) predictions for the tt-pair production at the Tevatron and LHC colliders and it is verified that the initial scale independence of the PMC prediction is satisfied to high accuracy at the NNLO level.

Abstract

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 $\{β_i\}$-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 $μ^{\rm PMC}_R$ and the resulting finite-order PMC prediction are both to high accuracy independent of the choice of initial renormalization scale $μ^{\rm init}_R$, 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 $σ_{t\bar{t}}$ 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 $μ^{\rm init}_R$ 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 $1\,σ$-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.

Figures (2)

• Figure 1: Total cross-section $\sigma_{t\bar{t}}$ for the top quark pair production versus top quark mass.
• Figure 2: Comparison of the PMC prediction with the CDF data cdf2 for the $t\bar{t}$-pair forward-backward asymmetry for the whole phase-space. The left diagram is for $A_{FB}^{t\bar{t}}$ in the $t\bar{t}$-rest frame, the middle diagram is for $A_{FB}^{p\bar{p}}$ in the laboratory frame, and the right diagram is for $A_{FB}^{t\bar{t}}(M_{t\bar{t}}>450\; {\rm GeV})$. The Hollik and Pagani's results (HP) qedc2 using conventional scale setting are presented for a comparison. The result for D0 data d02 shows a similar behavior.