General description of New Physics in $t$, $b$ and boson Interactions and its Unitarity Constraints

We list all possible $dim=6$ CP conserving $SU(3)\times SU(2) \times U(1)$ gauge invariant operators which could be generated in case no new particles would be reachable in the future Colliders, and the only observable New Physics would be in the form of new interactions affecting the scalar sector and the quarks of the third family. These operators involve the standard model scalar field, the electroweak gauge bosons and the quarks of the third family and the gluon. Subsequently, we identify those operators which do not contribute to LEP1 (and lower energy) observables at tree level. Since present measurements allowed the couplings of these operators to be rather large, we study the constraints on them induced by unitarity considerations.