We discuss our recently proposed S3(down)xS3(up) flavour-permutation-symmetric mixing observables, giving expressions for them in terms of (moduli-squared) of the mixing matrix elements. We outline their successful use in providing flavour-symmetric
descriptions of (non-flavour-symmetric) lepton mixing schemes. We develop our partially unified flavour-symmetric description of both quark and lepton mixings, providing testable predictions for CP-violating phases in both B decays and neutrino oscillations.
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 fermi
on 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.
