Application of the Principle of Maximum Conformality to Top-Pair Production

TL;DR

This paper applies the Principle of Maximum Conformality (PMC) to top-quark pair production to eliminate renormalization-scale ambiguity in perturbative QCD predictions. By decomposing tt̄ production into partonic channels and absorbing β-dependent terms into the running coupling, the authors set channel-specific PMC scales for non-Coulomb and Coulomb contributions, improving convergence and greatly reducing residual scale dependence. The numerical results at Tevatron and LHC energies show cross-sections that rise modestly compared with conventional scale settings and align with experimental data, with explicit predictions for σ_tt̄ at 1.96, 7, and 14 TeV and reduced PDF/αs uncertainties. Overall, the PMC framework enhances the precision and robustness of QCD predictions for heavy-quark production and can be extended to other processes.

Abstract

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale $μ_r$. For example, by using the conventional way of setting $μ_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $σ_{t \bar{t}}$ with the uncertainty $Δσ_{t \bar{t}}/σ_{t \bar{t}}\sim ({}^{+3%}_{-4%})$ at the Tevatron and LHC even for the present NNLO level. The Principle of Maximum Conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict the $t \bar t$ cross-section $σ_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that $σ_{t\bar{t}}$ remains almost unchanged by varying $μ^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the $(q\bar{q})$-channel, which is dominant at the Tevatron, its NLO PMC scale is much smaller than the top-quark mass in the small $x$-region, and thus its NLO cross-section is increased by about a factor of two. In the case of the $(gg)$-channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by $\sim 20%$. As a result, a larger $σ_{t\bar{t}}$ is obtained in comparison to the conventional scale-setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we predict $σ_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb, $σ_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $σ_{\rm LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ pb. [full abstract can be found in the paper.]

Figures (5)

• Figure 1: Diagram for the top-quark pair production obtained from the convolution of the partonic subprocess cross-section $\hat{\sigma}_{ij}$ with the parton luminosities ${\cal L}_{ij}$.
• Figure 2: A "flow chart" which illustrates the PMC procedure.
• Figure 3: Cut diagrams for the $n^{(1,2)}_f$-terms and the Coulomb-terms for the $(q\bar{q})$-channel up to NNLO, where the solid circles stand for the light-quark loops.
• Figure 4: PMC coefficients of the $(q\bar{q})$-channel versus the subprocess collision energy $\sqrt{s}$, which determine the behavior of the NLO PMC scale $Q^{**}_1$. $Q=m_t=172.9$ GeV.
• Figure 5: Comparison with of the PMC coefficients for the $(gg)$- and $(q\bar{q})$- channels versus the subprocess collision energy $\sqrt{s}$. $Q=m_t=172.9$ GeV.