Abstract
We consider supersymmetric extensions of the standard model in which the usual R or matter parity gets replaced by another R or non-R discrete symmetry that explains the observed longevity of the nucleon and solves the μ problem of MSSM. In order to identify suitable symmetries, we develop a novel method of deriving the maximal ZN(R) symmetry that satisfies a given set of constraints. We identify R parity violating (RPV) and conserving models that are consistent with precision gauge unification and also comment on their compatibility with a unified gauge symmetry such as the Pati–Salam group. Finally, we provide a counter-example to the statement found in the recent literature that the lepton number violating RPV scenarios must have μ term and the bilinear κLHu operator of comparable magnitude.
Highlights
Low-energy supersymmetry is still one of the most attractive schemes for physics beyond the standard model (SM)
The huge ratio between the GUT and electroweak scales allows us to give compelling arguments for the observed longevity of the nucleon which is somewhat hard to understand in extensions of the SM with low cut-off, where higher-dimensional baryon and lepton number violating operators are not very much suppressed
A ZR4 symmetry [29,35], which solves the μ problem [28,29], has been proposed. These symmetries remain the simplest options to explain the longevity of the proton in supersymmetric extensions of the SM
Summary
Low-energy supersymmetry is still one of the most attractive schemes for physics beyond the standard model (SM). R symmetries play a special role in this context, since the order parameter for R symmetry breaking is the gravitino mass m3/2.1 without having to go into details of supersymmetry breaking, it is possible to estimate the amount by which discrete R symmetries are broken This enables one to make statements about the coefficients of the effective operators that arise through R symmetry breaking. (discrete) R symmetries are broken by the vacuum expectation value (VEV) of some “hidden sector” superpotential, which carries R charge 2qθ , where qθ denotes the R charge of the superspace coordinate θ , and possibly by further operators This allows for the possibility of residual non-R ZM symmetries, in particular for qθ > 1 [14].
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