Anomalies of Discrete Symmetries and Gauge Coupling Unification

The anomaly of a discrete symmetry is defined as the Jacobian of the path-integral measure. Assuming that the anomaly at low energies is cancelled by the Green-Schwarz (GS) mechanism at a fundamental scale, we investigate possible Kac-Moody levels for anomalous discrete family symmetries. As the first example, we consider discrete abelian baryon number and lepton number symmetries in the minimal supersymmetric standard model with the see-saw mechanism, and we find that the ordinary unification of gauge couplings is inconsistent with the GS conditions, indicating the possible existence of further Higgs doublets. We consider various recently proposed supersymmetric models with a non-abelian discrete family symmetry. In a supersymmetric example with $Q_{6}$ family symmetry, the GS conditions are such that the gauge coupling unification appears close to the Planck scale.Comment: 22 pages, 4 figures, many typos corrected, references added, published versio

Anomaly of discrete family symmetries and gauge coupling unification

Anomaly of discrete symmetries can be defined as the Jacobian of the path-integral measure. We assume that an anomalous discrete symmetry at low energy is remnant of an anomaly free discrete symmetry, and that its anomaly is cancelled by the Green-Schwarz(GS) mechanism at a more fundamental scale. If the Kac-Moody levels k_i assume non-trivial values, the GS cancellation conditions of anomaly modify the ordinary unification of gauge couplings. This is most welcome, because for a renormalizable model to be realistic any non-abelian family symmetry, which should not be hardly broken low-energy, requires multi SU(2)_L doublet Higgs fields. As an example we consider a recently proposed supersymmetric model with Q_6 family symmetry. In this example, k_2=1, k_3=3 satisfies the GS conditions and the gauge coupling unification appears close to the Planck scale.Comment: Talk given at the Summer Institute 2006 (SI2006), APCTP, Pohang, Korea. 23-30 Aug 200

Constraints on the Timeon Model

The timeon model recently proposed by Friedberg and Lee has a potential problem of flavor changing neutral currents (FCNCs) if the mass of the timeon is small. In order to avoid, we introduce a small dimensionless parameter to suppress FCNCs. Even in this case, we find that the timeon mass must be larger than 151 GeV to satisfy all the constraints from processes involving FCNCs in the quark sectors. We also extend the timeon model to the lepton sector and examine the leptonic processes.Comment: 10 pages, 1 figure, published version in PR