NATURAL-R PARITY CONSERVATION WITH HORIZONTAL SYMMETRIES - A 4 GENERATION MODEL

In most supersymmetric models the stability of the proton is ensured b y invoking R parity. A necessary ingredient to enforce R parity is the possibility of distinguishing the lepton superfields from the Higgs o nes. This is generally achieved either by assuming different charges u nder some matter parity, or by assigning the superfields to different representations of a unified gauge group. We want to put forward the i dea that the replica of the fermion generations, which constitute an i ntrinsic difference between the fermions and the Higgs superfields, ca n give a clue to understanding R parity as an accidental symmetry. Mor e ambitiously, we suggest a possible relation between proton stability and the actual number of fermion generations. We carry out our invest igation in the framework of non-Abelian horizontal gauge symmetries. W e identify SU(4)(H) as the only acceptable horizontal gauge group whic h can naturally ensure the absence of R-parity-violating operators, wi thout conflicting with other theoretical and phenomenological constrai nts. We analyze a version of the supersymmetric standard model equippe d with a gauged horizontal SU(4)(H), in which R parity is accidental. The model predicts four families of fermions, it allows for the dynami cal generation of a realistic hierarchy of fermion masses without any ad hoc choice of small Yukawa couplings; it ensures in a natural way t he heaviness of all the fourth family fermions (including the neutrino ), and it predicts a lower Limit for the tau-neutrino mass of a few eV . The scale of the breaking of the horizontal symmetry can be constrai ned rather precisely in a narrow window around similar to 10(11) GeV. Some interesting astrophysical and cosmological implications of the mo del are addressed as well.