Rare $\Lambda_b\to n l^+l^-$ decays in the relativistic quark-diquark picture

The form factors of the rare $\Lambda_b\to n l^+l^-$ decays are calculated in the framework of the relativistic quark-diquark picture of baryons with the consistent account of the relativistic effects. Their momentum transfer squared dependence is determined explicitly in the whole accessible kinematical range. The decay branching fractions, forward-backward asymmetries and the fractions of longitudinally polarized dileptons are determined. The branching fraction of the rare $\Lambda_b\to n\mu^+\mu^-$ decay are found to be ${\rm Br}(\Lambda_b\to n\mu^+\mu^-)=(3.75\pm0.38)\times10^{-8}$ and thus could be measured at the LHC. Prediction for the branching fraction of the rare radiative $\Lambda_b\to n \gamma$ decay is also given.