An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists

Non-Abelian discrete symmetries are used in particle physics to understand the three-generation flavor structure. They are considered the most attractive choice for a flavor sector, and possible origins of the symmetry can arise from an underlying theory. The book provides an explicit introduction to the group theoretical aspects of many concrete groups, enabling readers to apply this to other groups of interest.

Format: Paperback / softback
Length: 353 pages
Publication date: 24 February 2022
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

This comprehensive lecture note serves as a tutorial review of non-Abelian discrete groups, delving into their applications in particle physics. While Abelian discrete symmetries are commonly employed to regulate couplings in particle physics, particularly in the context of model building beyond the standard model, non-Abelian discrete symmetries have gained prominence in understanding the three-generation flavor structure. Non-Abelian discrete symmetries are widely regarded as the most attractive choice for the flavor sector due to their ability to explain various phenomena in the lepton mixing and quark masses.

Model builders have attempted to derive experimental values of quark and lepton masses, mixing angles, and CP phases by assuming non-Abelian discrete flavor symmetries for quarks and leptons. However, lepton mixing has already been extensively discussed in this context. Another intriguing topic of research is the potential origins of non-Abelian discrete symmetry for flavors. These origins can stem from an underlying theory, such as string theory or compactification via orbifolding, resulting in geometrical symmetries like modular symmetries. By providing a bridge between the underlying theory and the corresponding low-energy sector of particle physics, these symmetries offer valuable insights.

The book provides an explicit introduction to the group theoretical aspects of numerous concrete groups, enabling readers to derive conjugacy classes, characters, representations, tensor products, and automorphisms for these groups (with a finite number) when algebraic relations are provided. Furthermore, CP symmetry and modular symmetry are presented, further enhancing the understanding of these complex concepts.

In conclusion, this lecture note offers a valuable resource for students and researchers interested in non-Abelian discrete groups and their applications in particle physics. By exploring the theoretical aspects and practical applications of these symmetries, readers gain a deeper understanding of the fundamental principles governing particle interactions and the construction of theoretical models.

Weight: 563g
Dimension: 235 x 155 (mm)
ISBN-13: 9783662646786
Edition number: 2nd ed. 2022