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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 with Yukawa-like terms, which proves to be a rich framework, with distinct aspects of CP, making it an ideal group to investigate with the invariant approach. We classify Lagrangians depending on the number of fields transforming as irreducible triplet representations of $Delta(27)$. For each case, we construct CP-odd weak basis invariants and use them to discuss the respective CP properties. We find that CP violation is sensitive to the number and type of $Delta(27)$ representations.
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 exampl
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 propose a simple framework based on $Delta(27)$ that leads to the successful cobimaximal lepton mixing ansatz, thus providing a predictive explanation for leptonic mixing observables. We explore first the effective neutrino mass operators, then pr
The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal, putting leptonic mixing in contrast with the small mixing of the quark sector. We discuss a model in whi
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