Abstract
We investigate the exclusive rare baryonic Lambda(b) -> Lambda l(+)Lambda l(-) decay in a family non-universal Z' model, which is one of the natural extensions of the Standard Model. Using transition form factors, calculated in the framework of light-cone QCD sum rules, we analyze the effects of polarized and unpolarized CP-violation asymmetries on the above-mentioned semileptonic decays of the Lambda(b) baryon. Our results indicate that the values of unpolarized and polarized CP-violation asymmetries are considerable in both the Lambda(b) -> Lambda mu(+)mu(-) and Lambda(b) -> Lambda tau(+)tau(-) channels, and hence they give a clear indication of new physics arising from the neutral Z' gauge boson. It is hoped that the measurements of these CP-violating asymmetries will not only help us to find hints of new physics, but also provide a tool to determine the precise values of the parameters of the Z' gauge boson.