Neutrinoless double beta decays of the top quark and other effects of heavy Majorana neutrinos

We discuss the rare decay of the top quark into a pair of same charge leptons (with identical or different flavors), a b quark and a (real or virtual) W-. The above process proceeds only if the exchanged neutrino N is of the Majorana type. This decay is the neutrinoless double b decay of the top. We find measurable values for its rate at the LHC with luminosity of 100 inverse fb. Furthermore, we consider an interaction of charged Higgs bosons with N which leads to lepton number violating processes such as pp to l+ N to l+ l+ H-, exhibiting spectacular events of the type: l+ l+ b b(bar) + 2 jets.