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

Abstract

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale ${\mu }_r$. For example, by using the conventional way of setting ${\mu }_r\in [m_t/2,2m_t]$, one obtains the total $t\bar{t}$ production cross-section ${\sigma }_{t\bar{t}}$ with the uncertainty \Delta \sigma_{t \bar{t}}/\sigma_{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 ${\sigma }_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that ${\sigma }_{t\bar{t}}$ remains almost unchanged by varying ${\mu }_r^{\mathrm{init}}$ 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 ${\sigma }_{t\bar{t}}$ 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 ${\sigma }_{\mathrm{Tevatron},1.96\mathrm{TeV}}=7.626_{-0.257}^{+0.265}$ pb, ${\sigma }_{\mathrm{LHC},7\mathrm{TeV}}=171.8_{-5.6}^{+5.8}$ pb and ${\sigma }_{\mathrm{LHC},14\mathrm{TeV}}=941.3_{-26.5}^{+28.4}$ pb. [full abstract can be found in the paper.]

Comments: 15 pages, 11 figures, 5 tables. Fig.(9) is corrected