Non-Abelian Discrete Symmetries in Particle Physics

By H. Ishimori, Tatsuo C. Kobayashi, H. Ohki, H. Okada, Yusuke Shimizu, M. Tanimoto. 2010

903 citations recorded by the source corpus.

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for SN , AN , T ′, DN , QN , Σ(2N 2), ∆(3N2), T7, Σ(3N 3) and ∆(6N2), which have been applied for model building in the particle physics. We also present typical flavor models by using A4, S4, and ∆(54) groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e99881dabcfae9eae446e022170c3302debeff86

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

1. Z. Xing
2. A. Titov
3. P. Novichkov
4. S. Petcov
5. J. Penedo
6. P. O. Ludl
7. Jure Zupan
8. Joachim Kopp

In Statistical and Nonlinear Physics

1. Z. Xing
2. S. Petcov
3. J. Penedo
4. P. Novichkov
5. A. Titov
6. Jure Zupan
7. Joachim Kopp
8. R. Harnik

Citations in the corpus

• Building and testing models with extended Higgs sectors (2017, methodology): “For an introduction to finite groups and formulas useful for model building, see for example reviews [130, 314].”
• Generalised CP symmetry in modular-invariant models of flavour (2019, background): “[2, 21,47,48]).”
• Search for lepton-flavour-violating decays of the Higgs boson (2015, neutral): “They also arise in supersymmetric models [6–9], composite Higgs boson models [10,11], models with flavour symmetries [12], Randall–Sundrum models [13–15], and many others [16–23].”