Predictions for the Top-Quark Forward-Backward Asymmetry at High Invariant Pair Mass Using the Principle of Maximum Conformality

摘要

The D0 collaboration at FermiLab has recently measured the top-quark pairforward-backward asymmetry in $\bar p p \to t \bar{t} X$ reactions as afunction of the $t\bar{t} $ invariant mass $M_{t\bar{t}}$. The D0 result for$A_{\rm FB}(M_{t\bar{t}}>650\, {\rm GeV})$ is smaller than $A_{\rmFB}(M_{t\bar{t}})$ obtained for small values of $M_{t\bar{t}}$, which mayindicate an "increasing-decreasing" behavior for $A_{\rmFB}(M_{t\bar{t}}>M_{\rm cut})$. This behavior is not explained usingconventional renormalization scale-setting, even by a next-to-next-to-leadingorder (N$^2$LO) QCD calculation -- one predicts a monotonically increasingbehavior. In the conventional scale-setting method, one simply guesses a singlerenormalization scale $\mu_r$ for the argument of the QCD running coupling andthen varies it over an arbitrary range. However, the conventional method hasinherent difficulties. ...... In contrast, if one fixes the scale using thePrinciple of Maximum Conformality (PMC), the resulting pQCD predictions arerenormalization-scheme independent since all of the scheme-dependent$\{\beta_i\}$-terms in the QCD perturbative series are resummed into the QCDrunning couplings at each order. ...... In this paper we show that if oneapplies the PMC to determine the top versus anti-top quark forward-backwardasymmetry by properly using the pQCD predictions up to N$^2$LO level, oneobtains the predictions without renormalization scheme or scale ambiguities....... In addition, the PMC prediction for $A_{\rm FB}(M_{t\bar{t}}> M_{\rmcut})$ shows an "increasing-decreasing" behavior for increasing values of$M_{\rm cut}$ which is not observed in the NLO and N$^2$LO predictions for$A_{\rm FB}(M_{t\bar{t}}> M_{\rm cut})$ with conventional scale-setting. Thisbehavior could be tested by the future more precise measurements at the LHC.