Is flavor discrete?

TL;DR

This paper examines the role of discrete symmetries in explaining leptonic flavor structures, comparing traditional and modular approaches, and discusses the challenges and potential extensions of these models.

Contribution

It analyzes the limitations of minimal discrete symmetry models and explores alternative approaches involving hidden sectors and additional physics.

Findings

Minimal models with few parameters are insufficient.

Complicated symmetry prescriptions introduce new free parameters.

Hidden sector interactions offer promising extensions.

Abstract

Relevance of the discrete symmetries for explanation of the observed flavor structures in the leptonic sector is considered. Achievements of the "traditional'' discrete symmetry approach and the modular symmetry approach are confronted. Minimal models with small number of parameters do not work. Complication of symmetry prescriptions allow to introduce new free parameters and thus describe the data but simultaneously bring two connected problems: (i) problem of "missing" representations, and (ii) problem of selection of certain point in huge discrete parameter space formed by possible charge assignments. Both problems must be addressed in complete model. Alternatively, one can keep minimal symmetry prescription but extend models introducing new physics unrelated to the original flavor symmetry. The low energy predictions can be "polluted" by additional physics such as effects of coupling to hidden sector, RGE running, decoupling of heavy degrees of freedom, mixing with sterile neutrinos, {\it etc.} The set up with discrete symmetries in the Hidden sector which communicates to the visible one via the neutrino portal and the basis fixing symmetry still looks promising.