Lepton number, black hole entropy and 10 to the 32 copies of the Standard Model

Abstract

Lepton number violating processes are a typical problem in theories with a low quantum gravity scale. In this paper 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. Naively one would expect black holes to introduce TeV scale LNV operators, thus generating unacceptably large rates of LNV processes. We show, however, that this does not happen in this scenario due to a complicated compensation mechanism between contributions of different Majorana neutrino states to these processes. As a result rates of LNV processes are extremely small and far beyond experimental reach, at least for the left-handed neutrino states.