Longitudinal top polarization as a probe of a possible origin of forward-backward asymmetry of the top quark at the Tevatron

If the forward-backward (FB) asymmetry of top quark ($A_{\rm FB}$) observed at the Tevatron deviates from the SM prediction, there must be $P$-violating interactions in $q\bar{q} \rightarrow t\bar{t}$. This new interaction will necessarily affect the top spin polarization. In this letter, we perform a model independent analysis on the longitudinal (anti)top polarization ($P_L$ and $\bar{P}_L$) using an effective lagrangian with dim-6 four-quark operators relevant for $q \bar{q} \rightarrow t \bar{t}$, and show that the $P$-odd observable corresponding to the polarization difference $(P_L - \bar{P}_L)$ gives important informations on the chiral structures of new physics that might be relevant to the $A_{\rm FB}$.