Plaquette Invariants and the Flavour Symmetric Description of Quark and Neutrino Mixings

TL;DR

This paper introduces new flavour-permutation-symmetric observables called plaquette invariants, which help describe quark and neutrino mixings and reveal phenomenological symmetries, providing a basis-invariant framework for flavor physics.

Contribution

It presents a complete set of plaquette invariants expressed in terms of mixing matrix elements and mass matrices, enabling flavor-symmetric descriptions and constraints on fermion mixing.

Findings

Most plaquette invariants are consistent with zero in leptonic mixing.

Explicit weak-basis invariant constraints are constructed for valid mixing models.

The approach unifies quark and neutrino mixing descriptions under flavor symmetry.

Abstract

We present a complete set of new flavour-permutation-symmetric mixing observables. We give expressions for these "plaquette invariants", both in terms of the mixing matrix elements alone, and in terms of manifestly Jarlskog-invariant functions of fermion mass matrices. While these quantities are unconstrained in the Standard Model, we point out that remarkably, in the case of leptonic mixing, the values of most of them are consistent with zero, corresponding to certain phenomenological symmetries. We give examples of their application to the flavour-symmetric description of both lepton and quark mixings, showing for the first time how to construct explicitly weak-basis invariant constraints on the mass matrices, for a number of phenomenologically valid mixing ansatze.