Application of the Principle of Maximum Conformality to the Top-Quark Charge Asymmetry at the LHC (1410.1607v2)

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., $A_{\rm C}|{\rm 7 TeV;PMC} =\left(1.15^{+0.01}{-0.03}\right)\%$, $A_{\rm C}|{\rm 8 TeV;PMC} =\left(1.03^{+0.01}{+0.00}\right)\%$, and $A_{\rm C}|{\rm 14 TeV;PMC} =\left(0.62^{+0.00}{-0.02}\right)\%$. The corresponding predictions using conventional scale setting are: $A_{\rm C}|{\rm 7 TeV;Conv.} =\left(1.23^{+0.14}{-0.14}\right)\%$, $A_{\rm C}|{\rm 8 TeV;Conv.} =\left(1.11^{+0.17}{-0.13}\right)\%$, and $A_{\rm C}|{\rm 14 TeV;Conv.} =\left(0.67^{+0.05}{-0.05}\right)\%$. In these predictions, the scale errors are predicted by varying the initial renormalization and factorization scales in the ranges $\mu^{\rm init}r\in[m_t/2,2m_t]$ 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 $M_{t\bar{t}}>0.5 ~ {\rm TeV}$ and $\mu_f=\mu^{\rm init}r =m_t$, we obtain $A{\rm C}|{\rm 7 TeV;PMC}=2.67\%$, $A{\rm C}|{\rm 8 TeV;PMC}=2.39\%$, and $A{\rm C}|_{\rm 14 TeV;PMC}=1.28\%$.