Anomaly-Free Discrete Gauge Symmetries in Froggatt-Nielsen Models

Abstract

Discrete symmetries can forbid dangerous <i>B</i>- and <i>L</i>-violating operators in the supersymmetric Lagrangian. Due to the violation of global discrete symmetries by quantum gravity effects, the introduced discrete symmetry should be a remnant of a spontaneously broken local gauge symmetry. <br /> Demanding anomaly freedom of the high-energy gauge theory, we determine all family-independent anomaly-free <i>Z</i>_<i>N</i> symmetries which are consistent with the trilinear MSSM superpotential terms in Part I. We find one outstanding <i>Z</i>₆ symmetry, proton hexality <i>P</i>₆, which prohibits all <i>B</i>- and <i>L</i>-violating operators up to dimension five, except for the Majorana neutrino mass terms <i>LH_uLH_u</i>. <br /> In Part II, we combine the idea that a discrete symmetry should have a gauge origin with the scenario of Froggatt and Nielsen. We construct concise <i>U</i>(1)_<i>X</i> Froggatt-Nielsen models in which the <i>Z</i>₃ symmetry baryon triality, <i>B</i>₃, arises from <i>U</i>(1)_<i>X</i> breaking. We choose this specific discrete gauge symmetry because it allows for <i>R</i>-parity violating interactions; thus neutrino masses can be explained without introducing right-handed neutrinos. We find six phenomenologically viable <i>B</i>₃-conserving Froggatt-Nielsen models.