CP violation from finite groups
By Mu-Chun Chen, Maximilian Fallbacher, K. Mahanthappa, M. Ratz, A. Trautner. 2014
168 citations recorded by the source corpus.
Author(s): Chen, MC; Fallbacher, M; Mahanthappa, KT; Ratz, M; Trautner, A | Abstract: We discuss the origin of CP violation in settings with a discrete (flavor) symmetry G. We show that physical CP transformations always have to be class-inverting automorphisms of G. This allows us to categorize finite groups into three types: (i) Groups that do not exhibit such an automorphism and, therefore, in generic settings, explicitly violate CP. In settings based on such groups, CP violation can have pure group-theoretic origin and can be related to the complexity of some Clebsch-Gordan coefficients. (ii) Groups for which one can find a CP basis in which all the Clebsch-Gordan coefficients are real. For such groups, imposing CP invariance restricts the phases of coupling coefficients. (iii) Groups that do not admit real Clebsch-Gordan coefficients but possess a class-inverting automorphism that can be used to define a proper (generalized) CP transformation. For such groups, imposing CP invariance can lead to an additional symmetry that forbids certain couplings. We make use of the so-called twisted Frobenius-Schur indicator to distinguish between the three types of discrete groups. With δ(27), T ', and σ(72) we present one explicit example for each type of group, thereby illustrating the CP properties of models based on them. We also show that certain operations that have been dubbed generalized CP transformations in the recent literature do not lead to physical CP conservation. © 2014 The Authors.
Subfields: Condensed Matter Physics, Nuclear and High Energy Physics, Plant Science
View Paper: https://www.semanticscholar.org/paper/daeeddc0f16faf9c8f781d97d84149dafbef95f0
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In Nuclear and High Energy Physics
Citations in the corpus
- Unification of flavor, CP, and modular symmetries (2019, background): “3 A CP-like transformation is a transformation that acts like a physical CP transformation on some but not all states of a theory [4].”
- Neutrino masses and mixing from double covering of finite modular groups (2019, background): “Discrete flavor symmetry in combination with generalized CP symmetry can give rise to rather predictive models [2–10], see [11] for a detailed list of references.”
- Neutrino non-standard interactions: A status report (2019, background): “Specifically, CP violation can be entirely group theoretical in origin [77], due to the existence of complex Clebsch-Gordan coefficients in certain non-Abelian discrete symmetries [78], leading to a rather predictive framework, in addition to providing a deep possible connection between residual spa”
- Flavor structures of charged fermions and massive neutrinos (2019, background): “The overall group constituted by GFS and HCP is therefore isomorphic to their semi-direct product GFS o HCP [1003, 1004, 1006].”
- Generalised CP symmetry in modular-invariant models of flavour (2019, background): “g′ and g−1 belong to the same conjugacy class [38].”
- Building and testing models with extended Higgs sectors (2017, background): “ far. Finally, we remark that there is a deeper mathematical relation between CP-symmetries and the automorphism group of G, the transformations which can be viewed as \symmetries of symmetries" [252, 340, 341, 342]. 3HDMs can accommodate not only new forms of CP-violation but also an exotic fo”