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

摘要

The Principle of Maximum Conformality (PMC) provides a systematic andprocess-independent method to derive renormalization scheme- and scale-independent fixed-order pQCD predictions. In Ref.\cite{pmc3}, we studied thetop-quark charge asymmetry at the Tevatron. By applying the PMC, we have shownthat the large discrepancies for the top-quark charge asymmetry between theStandard Model estimate and the CDF and D0 data are greatly reduced. In thepresent paper, with the help of the Bernreuther-Si program, we present adetailed PMC analysis on the top-quark pair production up tonext-to-next-to-leading order level at the LHC. After applying PMC scalesetting, the pQCD prediction for the top-quark charge asymmetry at the LHC hasvery 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 usingconventional 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 errorsare predicted by varying the initial renormalization and factorization scalesin the ranges $\mu^{\rm init}_r\in[m_t/2,2m_t]$ and $\mu_f\in[m_t/2,2m_t]$. ThePMC predictions are also in better agreement with the available ATLAS and CMSdata. In addition, we have calculated the top-quark charge asymmetry assumingseveral typical cuts on the top-pair invariant mass $M_{t\bar{t}}$. Forexample, assuming $M_{t\bar{t}}>0.5 ~ {\rm TeV}$ and $\mu_f=\mu^{\rm init}_r=m_t$, we obtain $A_{\rm C}|_{\rm 7 TeV;PMC}=2.67\%$, $A_{\rm C}|_{\rm 8TeV;PMC}=2.39\%$, and $A_{\rm C}|_{\rm 14 TeV;PMC}=1.28\%$.