Discrete symmetries and models of flavor mixing

TL;DR

This paper explores the role of discrete symmetries in explaining lepton and quark flavor mixing patterns, discussing theoretical frameworks, challenges, and potential experimental tests.

Contribution

It provides a comprehensive analysis of how discrete symmetries can underpin flavor mixing models and discusses extending these ideas to quarks and grand unified theories.

Findings

Discrete symmetries can explain lepton mixing patterns.

Challenges include flavor symmetry breaking and model consistency.

Future experiments can test symmetry-based predictions.

Abstract

Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, {\it ad hoc} prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In this connection the quark-lepton complementarity could be a viable alternative to TBM. Observational consequences of the symmetries and future experimental tests of their existence are discussed.