Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC

Abstract

The Principle of Maximum Conformality (PMC) provides a systematic and process-independent method to derive renormalization scheme- and scale- independent fixed-order pQCD predictions. In Ref.\cite{pmc3}, we studied the top-quark charge asymmetry at the Tevatron. By applying the PMC, we have shown that the large discrepancies for the top-quark charge asymmetry between the Standard Model estimate and the CDF and D0 data are greatly reduced. In the present paper, with the help of the Bernreuther-Si program, we present a detailed PMC analysis on the top-quark pair production up to next-to-next-to-leading order level at the LHC. After applying PMC scale setting, the pQCD prediction for the top-quark charge asymmetry at the LHC has very small scale uncertainty; e.g., $A_{\mathrm{C}}{|}_{7TeV;\mathrm{PMC}}=\left(1.15_{-0.03}^{+0.01}\right)\%$, $A_{\mathrm{C}}{|}_{8TeV;\mathrm{PMC}}=\left(1.03_{+0.00}^{+0.01}\right)\%$, and $A_{\mathrm{C}}{|}_{14TeV;\mathrm{PMC}}=\left(0.62_{-0.02}^{+0.00}\right)\%$. The corresponding predictions using conventional scale setting are: $A_{\mathrm{C}}{|}_{7TeV;Conv.}=\left(1.23_{-0.14}^{+0.14}\right)\%$, $A_{\mathrm{C}}{|}_{8TeV;Conv.}=\left(1.11_{-0.13}^{+0.17}\right)\%$, and $A_{\mathrm{C}}{|}_{14TeV;Conv.}=\left(0.67_{-0.05}^{+0.05}\right)\%$. In these predictions, the scale errors are predicted by varying the initial renormalization and factorization scales in the ranges ${\mu }_r^{\mathrm{init}}\in [m_t/2,2m_t]$ and ${\mu }_f\in [m_t/2,2m_t]$. The PMC predictions are also in better agreement with the available ATLAS and CMS data. In addition, we have calculated the top-quark charge asymmetry assuming several typical cuts on the top-pair invariant mass $M_{t\bar{t}}$. For example, assuming $M_{t\bar{t}}>0.5\mathrm{TeV}$ and ${\mu }_f={\mu }_r^{\mathrm{init}}=m_t$, we obtain $A_{\mathrm{C}}{|}_{7TeV;\mathrm{PMC}}=2.67\%$, $A_{\mathrm{C}}{|}_{8TeV;\mathrm{PMC}}=2.39\%$, and $A_{\mathrm{C}}{|}_{14TeV;\mathrm{PMC}}=1.28\%$.

Comments: 10 pages, 4 figures. Discussion improved