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General expressions for the double-lepton polarizations in the (B -> K l^+l^-) decay are obtained, using model independent effective Hamiltonian,including all possible interactions. Correlations between the averageddouble-lepton polarization asymmetries and the branching ratio, as well as, theaveraged single-lepton polarization asymmetry are studied. It is observed that,study of the double-lepton polarization asymmetries can serve as a good testfor establishing new physics beyond the Standard Model.Comment: 21 pages, 18 figures, LaTeX formatte

Double-lepton polarization asymmetries in the $B \to K \ell^ + \ell^-$ decaybeyond the standard model