Solutions to large B and L breaking in the Randall–Sundrum model

Abstract The stability of proton and neutrino masses are discussed in the Randall–Sundrum model. We show that relevant operators should be suppressed, if the hierarchical Yukawa matrices are explained only by configurations of wavefunctions for fermions and the Higgs field along the extra dimension. We assume a Z N discrete gauge symmetry to suppress those operators. In the Dirac neutrino case, there is an infinite number of symmetries which may forbid the dangerous operators. In the Majorana neutrino case, the discrete gauge symmetries should originate from U ( 1 ) X gauge symmetries which are broken on the Planck brane. We also comment on the n − n ¯ oscillation as a phenomenon which can distinguish those discrete gauge symmetries.