Neutrinoless double β 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 β decay of the top. We find measurable values for its rate at the LHC with luminosity of 100fb−1. Furthermore, we consider an interaction of charged Higgs bosons with N which leads to lepton number violating processes such as pp → lN → l+l+H−, exhibiting spectacular events of the type l+l+bb̄+ 2 jets.