The Top Forward Backward Asymmetry with general Z ' couplings

The measurement of the top forward-backward asymmetry in $\ttbar$ production measured at the Tevatron shows deviation from the Standard Model prediction. A $ u \to t$ transition via a flavor changing $Z^{\prime}$ can explain the data. We show that left handed $t_Lu_LZ^{\prime}$ couplings can be constrained from $B_{d,s}$ mixing while the constrains on the right handed couplings $t_R u_R Z^{\prime}$ vanish in the limit of $m_u \to 0$. We then consider the most general form of the $t uZ^{\prime}$ interaction which includes vector-axial vector as well as tensor type couplings and study how these couplings affect the top forward-backward asymmetry.