Patterns of remnant discrete symmetries

We analyze patterns of remnant discrete symmetries that arise from U(1)^N theories by spontaneous breaking. We describe a simple, geometrical way to understand these patterns and provide methods for identifying the discrete symmetries and bringing them to the simplest possible form. Applications in GUT and string model building are briefly discussed.Comment: 14 pages, 2 figures, a related Mathematica package can be downloaded from http://einrichtungen.physik.tu-muenchen.de/T30e/codes/DiscreteBreaking

Running minimal flavor violation

We consider the flavor structure of the minimal supersymmetric standard model (MSSM) in the framework of `minimal flavor violation' (MFV). We show that, if one imposes the MFV structure at some scale, to a good accuracy the MFV decomposition works at all other scales. That is, quantum effects can be described by running coefficients of the MFV decomposition. We find that the coefficients get driven to non-trivial fixed points.Comment: 13 pages, 12 figure

A unique Z_4^R symmetry for the MSSM

We consider the possible anomaly free Abelian discrete symmetries of the MSSM that forbid the mu-term at perturbative order. Allowing for anomaly cancellation via the Green-Schwarz mechanism we identify discrete R-symmetries as the only possibility and prove that there is a unique Z_4^R symmetry that commutes with SO(10). We argue that non-perturbative effects will generate a mu-term of electroweak order thus solving the mu-problem. The non-perturbative effects break the Z_4^R symmetry leaving an exact Z_2 matter parity. As a result dimension four baryon- and lepton-number violating operators are absent while, at the non-perturbative level, dimension five baryon- and lepton-number violating operators get induced but are highly suppressed so that the nucleon decay rate is well within present bounds.Comment: 6 page

Discrete R symmetries for the MSSM and its singlet extensions

We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with SU(5) and suppress the $\mu$ parameter and nucleon decay. We show that the order M of such $Z_M^R$ symmetries has to divide 24 and identify 5 viable symmetries. The simplest possibility is a $Z_4^R$ symmetry which commutes with SO(10). We present a string-derived model with this $Z_4^R$ symmetry and the exact MSSM spectrum below the GUT scale; in this model $Z_4^R$ originates from the Lorentz symmetry of compactified dimensions. We extend the discussion to include the singlet extensions of the MSSM and find $Z_4^R$ and $Z_8^R$ are the only possible symmetries capable of solving the $\mu$ problem in the NMSSM. We also show that a singlet extension of the MSSM based on a $Z_{24}^R$ symmetry can provide a simultaneous solution to the $\mu$ and strong CP problem with the axion coupling in the favoured window.Comment: 44+1 pages, 2 figure