We examine various solutions of the strong-CP problem to determine their sensitivity to possible violations of global symmetries by Planck scale physics.While some solutions remain viable even in the face of such effects, violations of the Peccei-Quinn (PQ) symmetry by non-renormalizable operators of dimension less than 10 will generally shift the value of θ to values inconsistent with the experimental bound θ < ∼ 10 −9 . We show that it is possible to construct axion models where gauge symmetries protect PQ symmetry to the requisite level.
The use of nonabelian discrete groups G as family symmetries is discussed in detail. Out of all such groups up to order g = 31, the most appealing candidates are two subgroups of SU (2)
We present the Mathematica application "LieART" (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART's user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.
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