Lepton number violation in theories with a large number of standard model copies

Abstract

We examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. On the other hand, the violation of the lepton number can be a potential phenomenological problem of this $N$-copy extension of the standard model as due to the low quantum gravity scale black holes may induce TeV scale LNV operators generating unacceptably large rates of LNV processes. We show, however, that this issue can be avoided by introducing a spontaneously broken ${U}_{1(B\ensuremath{-}L)}$. Then, due to the existence of a specific compensation mechanism between contributions of different Majorana neutrino states, LNV processes in the standard model copy become extremely suppressed with rates far beyond experimental reach.