Controlled flavor violation in the MSSM from a unified $\Delta(27)$ flavor symmetry

TL;DR

This paper explores a supersymmetric model with a $ ext{Δ}(27)$ flavor symmetry that explains quark and lepton masses and mixings, predicts flavor violation effects, and can be tested in future experiments.

Contribution

It introduces a unified texture zero structure in mass matrices within a $ ext{Δ}(27)$ symmetric MSSM, linking flavor observables to supersymmetric flavor violation.

Findings

The model reproduces known quark and lepton mixing patterns.

Large flavor violating effects are predicted due to non-universal soft terms.

Parameter space constraints can be tested by upcoming flavor violation experiments.

Abstract

We study the phenomenology of a unified supersymmetric theory with a flavor symmetry $\Delta(27)$. The model accommodates quark and lepton masses, mixing angles and CP phases. In this model, the Dirac and Majorana mass matrices have a unified texture zero structure in the $(1,1)$ entry that leads to the Gatto-Sartori-Tonin relation between the Cabibbo angle and ratios of the masses in the quark sectors, and to a natural departure from zero of the $\theta_{13}^\ell$ angle in the lepton sector. We derive the flavor structures of the trilinears and soft mass matrices, and show their general non-universality. This causes large flavor violating effects. As a consequence, the parameter space for this model is constrained, allowing it to be (dis)proven by flavor violation searches in the next decade. Although the results are model specific, we compare them to previous studies to show similar flavour effects (and associated constraints) are expected in general in supersymmetric flavor models, and may be used to distinguish them.