Application of the principle of maximum conformality to the top-quark forward-backward asymmetry at the Tevatron

The renormalization scale uncertainty can be eliminated by the principle of maximum conformality (PMC) in a systematic, scheme-independent way. Applying the PMC for the tt¯-pair hadroproduction at the next-to-next-to-leading-order level, we have found that the total cross sections σ_tt¯ at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales μ_R^init equal to m_t, 10m_t, 20m_t and s, which is consistent with renormalization group invariance. As an important new application, we apply PMC scale setting to study the top quark forward-backward asymmetry. We observe that the more convergent perturbative series after PMC scale-setting leads to a more accurate top quark forward-backward asymmetry. The resulting PMC prediction on the asymmetry is also free from the initial renormalization scale dependence. Because the next-to-leading-order PMC scale has a dip behavior for the (qq¯) channel at small subprocess collision energies, the importance of this channel to the asymmetry is increased. We observe that the asymmetries A_FB^tt¯ and A_FB^pp¯ at the Tevatron will be increased by 42% in comparison to the previous estimates obtained by using conventional scale setting; i.e., we obtain A_FB^tt¯,PMC≃12.5% and A_FB^pp¯,PMC≃8.28%. Moreover, we obtain A_FB^tt¯,PMC(M_tt¯>450GeV)≃35.0%. These predictions have a 1σ deviation from the present CDF and D0 measurements; the large discrepancies of the top quark forward-backward asymmetry between the standard model estimate and the CDF and D0 data are thus greatly reduced.