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 {mu}{sub r}. For example, by using the conventional way of setting {mu}{sub r} {element_of} [m{sub t}/2, 2m{sub t}], one obtains the total t{bar t} production cross-section {sigma}{sub t{bar t}} with the uncertainty {Delta}{sigma}{sub t{bar t}}/{sigma}{sub t{bar t}} {approx} (+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. By using the PMC, all nonconformal {l_brace}{beta}{sub i}{r_brace}-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{sub f} in the {l_brace}{beta}{sub i}{r_brace}-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 {mu}{sub r}{sup init}. The PMC scale {mu}{sub r}{sup PMC} is unambiguous at finite order. Any residual dependence on {mu}{sub r}{sup init} for a finite-order calculation will be highly suppressed since the unknown higher-order {l_brace}{beta}{sub i}{r_brace}-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 {sigma}{sub t{bar t}} at the NNLO level. In this paper we apply PMC scale-setting to predict the t{bar t} cross-section {sigma}{sub t{bar t}} at the Tevatron and LHC colliders. It is found that {sigma}{sub t{bar t}} remains almost unchanged by varying {mu}{sub r}{sup init} within the region of [m{sub t}/4, 4m{sub 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 {radical}s, but it is still smaller than m{sub t} for {radical} {approx}< 1 TeV, and the resulting NLO cross-section is increased by {approx}20%. As a result, a larger {sigma}{sub 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{sub t} = 172.9 {+-} 1.1 GeV, we predict {sigma}{sub Tevatron, 1.96 TeV} = 7.626{sub -0.257}{sup +0.265} pb, {sigma}{sub LHC, 7 TeV} = 171.8{sub -5.6}{sup +5.8} pb and {sigma}{sub LHC, 14 TeV} = 941.3{sub -26.5}{sup +28.4} pb.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); Program for New Century Excellent Talents in University under Grant NO.NCET-10-0882, Natural Science Foundation of China under Grant NO.11075225
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 1038419
- Report Number(s):
- SLAC-PUB-14888; arXiv:1204.1405; TRN: US1201855
- Journal Information:
- Phys.Rev.D86:014021,2012, Vol. 86, Issue 1; ISSN 1550--7998
- Country of Publication:
- United States
- Language:
- English
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