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 pair forward-backward asymmetry in (p) over barp -> t (t) over barX reactions as a function of the t (t) over bar invariant mass M-t (t) over bar. The D0 result for A(FB)(M-t (t) over bar) > 650 GeV) is smaller than A(FB)(M-t (t) over bar) obtained for small values of M-tt, which may indicate an "increasing-ecreasing" behavior for A(FB)(M-t (t) over bar > M-cut). This behavior is not explained using conventional renormalization scale setting, or even by a next-to-next-to-leading order ((NLO)-L-2) QCD calculation-one predicts a monotonically increasing behavior. In the conventional scale-setting method, one simply guesses a single renormalization scale mu(r) for the argument of the QCD running coupling and then varies it over an arbitrary range. However, the conventional method has inherent difficulties. For example, the resulting perturbative quantum chromodynamics (pQCD) predictions depend on the choice of renormalization scheme, in contradiction to the principle of "renormalization scheme invariance"-predictions for physical observables cannot depend on a theoretical convention. The error estimate obtained by varying mu(r) is unreliable since it is only sensitive to perturbative contributions involving the pQCD beta-function. Worse, guessing the renormalization scale gives predictions for precision QED observables which are in contradiction to results obtained using the standard Gell-Mann-Low method. In contrast, if one fixes the scale using the principle of maximum conformality (PMC), the resulting pQCD predictions are renormalization-scheme independent since all of the scheme-dependent {beta(i)}-terms in the QCD perturbative series are resummed into the QCD running couplings at each order. The {beta(i)}-terms at each order can be unambiguously identified using renormalization group methods such as the R-delta method. The PMC then determines the renormalization scales of the running coupling at each order and provides unambiguous scale-fixed and scheme-independent predictions. The PMC reduces in the N-C -> 0 Abelian limit to the standard Gell-MannLow scale-setting method used in QED, including precise scheme-independent predictions for the forward-backward symmetry of the e(+)e(-) -> mu(+)mu(-) cross section. By using the rigorous PMC scale-setting procedure, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the top-quark pair forward-backward asymmetry. In this paper we show that if one applies the PMC to determine the top versus antitop quark forward-backward asymmetry by properly using the pQCD predictions up to (NLO)-L-2 level, one obtains the predictions without renormalization-scheme or scale ambiguities. For example, the PMC predicts A(FB)(PMC) (M-t (t) over bar > 450 GeV) = 29.9% at the Tevatron, which is consistent with the CDF measurements. In addition, the PMC prediction for A(FB)(M-t (t) over bar > M-cut) shows an increasing-decreasing behavior for increasing values of M-cut which is not observed in the NLO and (NLO)-L-2 predictions for A(FB)(M-t (t) over bar > M-cut) with conventional scale setting. This behavior could be tested by the future more precise measurements at the LHC.