Top quark forward-backward asymmetry at approximate NLO3

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 $(6.8\ifmmode\pm\else\textpm\fi{}0.3)%$, and in the $t\overline{t}$ rest frame it is $(10.0\ifmmode\pm\else\textpm\fi{}0.6)%$ which is in excellent agreement with recent Tevatron data.