Abstract
Possible manifestation of the family non-universal Z' boson effects in lepton polarization in rare, exclusive baryonic "Lambda_b -> Lambda l+l-" decay is examined. It is observed that the double lepton polarizations P_TT and P_NN are sensitive to the Z' contribution. Moreover, it is found that the zero position of the polarized forward-backward asymmetry A_FB^LL is shifted to the left compared to the standard model prediction. Therefore, determination of the zero value of A_FB^LL is quite an efficient tool for establishing new Z' boson, but also in discriminating various scenarios of the considered family non-universal Z' model.
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