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We propose the use of basis invariants, valid for any choice of CP transformation, as a powerful approach to studying specific models of CP violation in the presence of discrete family symmetries. We illustrate the virtues of this approach for examples based on $A_4$ and $Delta(27)$ family symmetries. For $A_4$, we show how to elegantly obtain several known results in the literature. In $Delta(27)$ we use the invariant approach to identify how explicit (rather than spontaneous) CP violation arises, which is geometrical in nature, i.e. persisting for arbitrary couplings in the Lagrangian.
The invariant approach is a powerful method for studying CP violation for specific Lagrangians. The method is particularly useful for dealing with discrete family symmetries. We focus on the CP properties of unbroken $Delta(27)$ invariant Lagrangians
We use a new weak basis invariant approach to classify all the observable phases in any extension of the Standard Model (SM). We apply this formalism to determine the invariant CP phases in a simplified version of the Minimal Supersymmetric SM with o
We study the spontaneous $CP$ violation through the stabilization of the modulus $tau$ in modular invariant flavor models. The $CP$-invaraiant potentential has the minimum only at ${rm Re}[tau] = 0$ or 1/2. From this prediction, we study $CP$ violati
CP-odd invariants, independent of basis and valid for any choice of CP transformation are a powerful tool in the study of CP. They are particularly convenient to study the CP properties of models with family symmetries. After interpreting the consequ
We show how the SUSY flavour and CP problems can be solved using gauged SU(3) family symmetry previously introduced to describe quark and lepton masses and mixings, in particular neutrino tri-bimaximal mixing via constrained sequential dominance. The