Large Leptonic Dirac CP Phase from Broken Democracy with Random Perturbations

TL;DR

This paper proposes that broken democratic mass matrices with random perturbations, guided by residual symmetries, naturally produce large leptonic CP phases and realistic fermion mixing patterns, improving upon anarchic models.

Contribution

It introduces a framework where residual symmetries lead to democratic mass matrices with random perturbations, explaining large CP phases and realistic mixing angles.

Findings

Leptonic Dirac CP phase peaks around ±π/2 with perturbations.

Broken democracy models outperform anarchic models in predicting fermion properties.

Framework links residual symmetries to realistic fermion mass and mixing predictions.

Abstract

A large value of the leptonic Dirac CP phase can arise from broken democracy, where the mass matrices are democratic up to small random perturbations. Such perturbations are a natural consequence of broken residual $\mathbb S_3$ symmetries that dictate the democratic mass matrices at leading order. With random perturbations, the leptonic Dirac CP phase has a higher probability to attain a value around $\pm \pi/2$. Comparing with the anarchy model, broken democracy can benefit from residual $\mathbb S_3$ symmetries, and it can produce much better, realistic predictions for the mass hierarchy, mixing angles, and Dirac CP phase in both quark and lepton sectors. Our approach provides a general framework for a class of models in which a residual symmetry determines the general features at leading order, and where, in the absence of other fundamental principles, the symmetry breaking appears in the form of random perturbations.