Application of the Principle of Maximum Conformality to the Top-Quark Forward-Backward Asymmetry at the Tevatron

Abstract

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 $t\bar{t}$-pair hadroproduction at the NNLO level, we have found that the total cross-sections ${\sigma }_{t\bar{t}}$ at both the Tevatron and LHC remain almost unchanged when taking very disparate initial scales ${\mu }_R^{\mathrm{init}}$ equal to $m_t$, $10m_t$, $20m_t$ and $\sqrt{s}$, 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 NLO PMC scale has a dip behavior for the $(q\bar{q})$-channel at small subprocess collision energies, the importance of this channel to the asymmetry is increased. We observe that the asymmetries $A_{FB}^{t\bar{t}}$ and $A_{FB}^{p\bar{p}}$ at the Tevatron will be increased by 42% in comparison to the previous estimates obtained by using conventional scale-setting; i.e. we obtain $A_{FB}^{t\bar{t},\mathrm{PMC}}\simeq 12.5$ and $A_{FB}^{p\bar{p},\mathrm{PMC}}\simeq 8.28$. Moreover, we obtain $A_{FB}^{t\bar{t},\mathrm{PMC}}(M_{t\bar{t}}>450\mathrm{GeV})\simeq 35.0$. These predictions have a $1\sigma$-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.

Comments: 10 pages, 9 figures. To match the published version. To be published in Phys.Rev.D