Lepton polarization correlations in $\overrightarrow{B}{K}^{*}{\tau }^{-}{\tau }^{+}$

In this work we will study the polarizations of both leptons $\left(\tau \right)$ in the decay channel $\overrightarrow{B}{K}^{*}{\tau }^{-}{\tau }^{+}.$ In the case of the dileptonic inclusive decay $\overrightarrow{B}{K}^{*}{\mathcal{l}}^{-}{\mathcal{l}}^{+},$ where apart from the polarization asymmetries of a single lepton $\mathcal{l},$ one can also observe the polarization asymmetries of both leptons simultaneously. If this sort of measurement is possible then we can have, apart from decay rate, forward backward asymmetry and the six single lepton polarization asymmetries (three each for ${\mathcal{l}}^{-}$ and ${\mathcal{l}}^{+}),$ nine more double polarization asymmetries. This will give us a very useful tool in more strict testing of the standard model (SM) and the physics beyond. We discuss the double polarization asymmetries of the $\tau$ leptons in the decay mode $\overrightarrow{B}{K}^{*}{\tau }^{-}{\tau }^{+}$ within the SM and the minimal supersymmetric extension of it.