Forward-backward asymmetry and differential cross section of top quark in flavor violating $Z^{\mathrm{\prime }}$ model at $\mathcal{O}({\alpha }_s^2{\alpha }_X)$

In this paper, forward-backward asymmetry and differential cross section of top quark in flavor violating $Z^{\mathrm{\prime }}$ model up to $\mathscr{O}(\alpha_s^2 \alpha_X)$ at Tevatron are calculated. In order to account for the top observed large forward-backward asymmetry, the new coupling $g_X$ among $Z^{\mathrm{\prime }}$ and quarks will be not much less than strong coupling constant $g_s$. After including the new higher order correction, the differential cross section can fit the data better than those only including the leading contributions from $Z^{\mathrm{\prime }}$, while the forward-backward asymmetry is still in agreement with the measurement.