Natural R-parity, μ-term, and fermion mass hierarchy from discrete gauge symmetries

In the minimal supersynnnetric Standard Model with see-saw neutrino masses we show how R-parity can emerge naturally as a discrete gauge symmetry. The same discrete symmetry explains the smallness of the mu-term (the Higgsino mass parameter) via the Giudice-Masiero mechanism. The discrete gauge anomalies are cancelled by a discrete version of the Green-Schwarz mechanism. The simplest symmetry group is found to be Z(4) with a charge assignment that is compatible with grand unification. Several other Z(N) gauge symmetries are found for N = 10, 12, 18, 36 etc., with some models employing discrete anomaly cancellation at higher Kac-Moody levels. Allowing for a flavor structure in Z(N), we show that the same gauge symmetry can also explain the observed hierarchy in the fermion masses and mixings. (C) 2003 Elsevier Science B.V. All rights reserved.