In this work we shall derive expressions for the single and double lepton polarization asymmetries for the exclusive decay $B to K^* ell^+ ell^-$, using the most general model independent effective Hamiltonian. We have conducted this study with this particular channel as it has the highest branching ratio among the various purely leptonic and semi-leptonic decay modes, making this mode particularly useful for studying physics beyond the SM. We have also analyzed the effects on these polarization asymmetries, and hence the physics underlying it, when complex phases are included in some of the Wilson coefficients.
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