Top quark forward-backward asymmetry at approximate $\mathrm{N}{}^3\mathrm{LO}$

I calculate the top quark forward-backward asymmetry at the Tevatron in both the laboratory frame and the $t\overline{t}$ rest frame. I show that soft-gluon corrections are the dominant contribution to the asymmetry and closely approximate exact results through next-to-next-to-leading order (NNLO). I present a calculation of the asymmetry including approximate next-to-next-to-next-to-leading-order ($\mathrm{N}{}^3\mathrm{LO}$) soft-gluon contributions from next-to-next-to-leading-logarithm resummation as well as electroweak corrections. Thus approximate $\mathrm{N}{}^3\mathrm{LO}$ ($\mathrm{a}\mathrm{N}{}^3\mathrm{LO}$) results are obtained, which significantly enhance and improve previous NNLO results. The theoretical $\mathrm{a}\mathrm{N}{}^3\mathrm{LO}$ result for the top quark forward-backward asymmetry at the Tevatron in the laboratory frame is $(6.8\pm 0.3)\%$, and in the $t\overline{t}$ rest frame it is $(10.0\pm 0.6)\%$ which is in excellent agreement with recent Tevatron data.

Figure 1

The top quark forward-backward asymmetry at NNLO, aNNLO, and $\mathrm{a}\mathrm{N}{}^3\mathrm{LO}$ QCD (without EW corrections) as a function of $|\mathrm{\Delta }y|$ in $t\overline{t}$ production at the Tevatron with $\sqrt{S}=1.96\mathrm{TeV}$. The central lines at each order are with $\mu =m_t$, and the other lines display the upper and lower values from scale variation over $m_t/2\le \mu \le 2m_t$.

Figure 2

The top quark forward-backward asymmetry at $\mathrm{a}\mathrm{N}{}^3\mathrm{LO}$ QCD (without EW corrections) as a function of $|\mathrm{\Delta }y|$ and comparison with CDF [7] and D0 [8] data in $t\overline{t}$ production at the Tevatron with $\sqrt{S}=1.96\mathrm{TeV}$. The central $\mathrm{a}\mathrm{N}{}^3\mathrm{LO}$ lines are with $\mu =m_t$, and the other lines display the upper and lower values from scale variation over $m_t/2\le \mu \le 2m_t$.