Nonanomalous R-symmetry in supersymmetric unified theories of quarks and leptons

TL;DR

This paper investigates the existence of nonanomalous discrete R-symmetries in supersymmetric theories derived from higher-dimensional frameworks. In the MSSM, anomaly constraints plus the Giudice-Masiero mechanism permit two viable symmetries, $Z_{9R}$ and $Z_{18R}$, with certain SUSY-breaking residuals that affect LSP stability. When embedding quarks and leptons into SU(5) GUT multiplets, the anomalies typically reappear, necessitating extra matter; the simplest remedy is a pair of ${\bf 5}$ and ${\bf 5^*}$, which leads to nonanomalous $Z_{4R}$ or $Z_{20R}$ and motivates a concrete unification model based on $SU(5)_{\rm GUT}\times U(3)_H$ with TeV-scale exotics. The extra matter yields testable collider signatures and preserves suppression of dangerous operators, with broader implications for NMSSM and GMSB scenarios.

Abstract

A discrete R-symmetry often appears as an exact gauge symmetry in the low energy effective theory of superstring theories. We search for such discrete R-symmetries from a phenomenological point of view and find that Z_{9R} and Z_{18R} are candidates of the nonanomalous R-symmetry in the case of the minimal supersymmetric standard model. We also find Z_{4R} and Z_{20R} in the case that quarks and leptons are embedded in the SU(5) GUT multiplets. Interesting is that in the latter case all the solutions predict some extra matter multiplets and we find that the simplest choice is to take a pair of {\bf 5} and {\bf 5}^* of SU(5)_{GUT} whose mass is of order the SUSY breaking scale \sim 1 TeV. We emphasize that the presence of such extra matters is testable in future collider experiments.