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The top quark forward-backward asymmetry at approximate N$^3$LO

I calculate the top quark forward-backward asymmetry at the Tevatron in both the laboratory frame and the $t{\bar t}$ 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 (N$^3$LO) soft-gluon contributions from next-to-next-to-leading-logarithm (NNLL) resummation as well as electroweak corrections. Thus approximate N$^3$LO (aN$^3$LO) results are obtained, which significantly enhance and improve previous NNLO results. The theoretical aN$^3$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 $t{\bar t}$ rest frame it is ($10.0 \pm 0.6$)\% which is in excellent agreement with recent Tevatron data.