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 ₑ. For example, by using the conventional way of setting ₑmₓ/2, 2mₓ, one obtains the total tt production cross section ₓₓ with the uncertainty ₓₓ/ₓₓ (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 {₈} 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 n₅ in the {₈} 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 ₑ^init. The PMC scale ₑ^PMC is unambiguous at finite order. Any residual dependence on ₑ^init for a finite-order calculation will be highly suppressed since the unknown higher-order {₈} 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 ₓₓ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the tt cross section ₓₓ at the Tevatron and LHC colliders. It is found that ₓₓ remains almost unchanged by varying ₑ^init within the region of mₓ/4, 4mₓ. The convergence of the expansion series is greatly improved. For the (qq) 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 mₓ for s1 TeV, and the resulting NLO cross section is increased by 20%. As a result, a larger ₓₓ is obtained in comparison to the conventional scale setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting mₓ=172. 91. 1 GeV, we predict ₓ₄ₕ₀ₓₑ₎₍, ₁. ₉₆ ₓ₄ₕ=7. 626-₀. ₂₅₇^+0. 265 pb, ₋₇₂, ₇ ₓ₄ₕ=171. 8-₅. ₆^+5. 8 pb and ₋₇₂, ₁₄ ₓ₄ₕ=941. 3-₂₆. ₅^+28. 4 pb.