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 μ_r. For example, by using the conventional way of setting μ_r∈[m_t/2,2m_t], one obtains the total tt¯ production cross section σ_tt¯ with the uncertainty Δσ_tt¯/σ_tt¯∼((+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 {β_i} 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 n_f in the {β_i} 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 μ_r^init. The PMC scale μ_r^PMC is unambiguous at finite order. Any residual dependence on μ_r^init for a finite-order calculation will be highly suppressed since the unknown higher-order {β_i} 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 σ_tt¯ at the next-to next-to-leading-order level. In this paper we apply PMC scale setting to predict the tt¯ cross section σ_tt¯ at the Tevatron and LHC colliders. It is found that σ_tt¯ remains almost unchanged by varying μ_r^init within the region of [m_t/4,4m_t]. 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 m_t for s≲1TeV, and the resulting NLO cross section is increased by ∼20%. As a result, a larger σ_tt¯ 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±1.1GeV, we predict σ_{Tevatron,1.96TeV}=7.626_-0.257^+0.265pb, σ_LHC,7TeV=171.8_-5.6^+5.8pb and σ_LHC,14TeV=941.3_-26.5^+28.4pb.