Search for New Physics Through e^- e^+ to t bar t

If all new particles are too heavy to be directly produced in the future Colliders, then the long sought New Physics (NP) could only appear in the form of new interactions, beyond those of the Standard Model (SM). Many of the processes that could be used to study these interactions, have already been discussed in the literature. Here, I first briefly discuss the list of all not yet excluded CP conserving such interactions, realized as $SU(3)\times SU(2) \times U(1)$ gauge invariant $dim=6$ operators affecting the Higgs and the quarks of the third family. Subsequently, I concentrate on the $\gamma t\bar t$ and $Zt\bar t$ vertices generated by NP, and on the possibility to study them by using various spin asymmetries accessible in $e^-e^+ \to t \bar t$, for polarized and unpolarized beams. It is found that these asymmetries can fully determine the form of the $\gamma t\bar t$ and $Zt\bar t$ couplings.