W polarization in $e^{+}{e}^{-}$, gluon-gluon and $\gamma \gamma \to Wt\bar{b}$ for testing the top quark mass structure and the presence of final interactions

We analyze the $Wt\bar{b}$ production processes and especially the rate of longitudinal $W$ polarization sensitive to a possible top quark mass scale dependence and to the presence of strong final state $Wt$ interactions for example generated by a dark matter environment. We give illustrations for the three processes $e^{+}{e}^{-}$, gluon-gluon and $\gamma \gamma \to Wt\bar{b}$.