The mu term and neutrino masses

Abstract

The well-known Giudice-Masiero mechanism explains the presence of a mu term of the order of the gravitino mass, but does not explain why the holomorphic mass term is absent in the superpotential. We discuss anomaly-free discrete symmetries which are both compatible with SU(5) unification of matter and the Giudice-Masiero mechanism, i.e. forbid the mu term in the superpotential while allowing the necessary Kaehler potential term. We find that these are Z_M^R symmetries with the following properties: (i) M is a multiple of four; (ii) the Higgs bilinear H_u H_d transforms trivially; (iii) the superspace coordinate theta has charge M/4 and, accordingly, the superpotential has charge M/2; (iv) dimension five proton decay operators are automatically absent. All Z_M^R symmetries are anomaly-free due to a non-trivial transformation of a Green-Schwarz axion, and, as a consequence, a holomorphic mu term appears at the non-perturbative level. There is a unique symmetry that is consistent with the Weinberg operator while there is a class of Z_M^R symmetries which explain suppressed Dirac neutrino masses.

24 pages

References in corpus (11)

• Symmetries and Strings in Field Theory and Gravity
• Supersymmetry Breaking, R-Symmetry Breaking and Metastable Vacua
• Discrete R symmetries for the MSSM and its singlet extensions
• Retrofitting O'Raifeartaigh Models with Dynamical Scales
• A unique Z_4^R symmetry for the MSSM
• Patterns of remnant discrete symmetries
• Approximate R-symmetries and the mu term
• Multiple anomalous U(1)s in heterotic blow-ups
• Gauged Discrete Symmetries and Proton Stability
• Gauge symmetry breaking in orbifold model building
• SU(6) GUT Breaking on a Projective Plane

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