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We perform a comprehensive analysis of the rare "Lambda_b -> Lambda l+ l-"decay in the framework of family non-universal Z' model. It is shown that Z'gives considerable contribution to the decay width. Zero positions of theforward-backward asymmetry and alpha_theta parameter are shifted to the leftcompared to the Standard Model result. The obtained results could be tested innear future at LHC-b.

Lambda_b -> Lambda l+ l- decay within family non-universal Z' model