Application of the principle of maximum conformality to top-pair production

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale μᵣ. For example, by using the conventional way of setting μᵣ∈[mₜ/2,2mₜ], one obtains the total tt̄ production cross section σtt̄ with the uncertainty Δσtt̄/σtt̄~(0+3%-4%) at the Tevatron and LHC even for the present next-to next-to-leading-order level. The principle of maximum conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. By using the PMC, all nonconformal βᵢ terms in the perturbative expansion series are summed into the running coupling constant, and the resulting scale-fixed predictions are independent of the renormalization scheme. The correct scale displacement between the arguments of different renormalization schemes is automatically set, and the number of active flavors nf in the βᵢ function is correctly determined. The PMC is consistent with the renormalization group property that a physical result is independent of the renormalization scheme and the choice of the initial renormalization scale μᵣⁱⁿⁱᵗ. The PMC scale μᵣPMC is unambiguous at finite order. Any residual dependence on μᵣⁱⁿⁱᵗ for a finite-order calculation will be highly suppressed since the unknown higher-order βᵢ terms will be absorbed into the PMC scales' higher-order perturbative terms. We find that such renormalization group invariance can be satisfied to high accuracy for σtt̄ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the tt̄ cross section σtt̄ at the Tevatron and LHC colliders. It is found that σtt̄ remains almost unchanged by varying μᵣⁱⁿⁱᵗ within the region of [mₜ/4,4mₜ]. The convergence of the expansion series is greatly improved. For the (qq̄) channel, which is dominant at the Tevatron, its next-to-leading-order (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 2. In the case of the ($gg$) channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy √s, but it is still smaller than mₜ for √s1 TeV, and the resulting NLO cross section is increased by ~20%. As a result, a larger σtt̄ is obtained in comparison to the conventional scale setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting mₜ=172.9±1.1 GeV, we predict σTevatron,1.96 TeV=7.626_-0.257+0.265 pb, σLHC,7 TeV=171.8_-5.6+5.8 pb and σLHC,14 TeV=941.3_-26.5+28.4 pb.