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

Abstract

In the minimal supersymmetric 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 μ-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.