Natural R–Parity, μ–term, and Fermion Mass Hierarchy From Discrete Gauge Symmetries

In the minimal supersymmetric Standard Model with seesaw 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 Z4 with a charge assignment that is compatible with grand unification. Several other ZN 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 ZN , we show that the same gauge symmetry can also explain the observed hierarchy in the fermion masses and mixings. E-mail address: [email protected] 2 On leave of absence from: Andronikashvili Institute of Physics, GAS, 380077 Tbilisi, Georgia. E-mail address: [email protected] E-mail address: [email protected]