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We present a complete set of new flavour-permutation-symmetric mixingobservables. We give expressions for these "plaquette invariants", both interms of the mixing matrix elements alone, and in terms of manifestlyJarlskog-invariant functions of fermion mass matrices. While these quantitiesare unconstrained in the Standard Model, we point out that remarkably, in thecase of leptonic mixing, the values of most of them are consistent with zero,corresponding to certain phenomenological symmetries. We give examples of theirapplication to the flavour-symmetric description of both lepton and quarkmixings, showing for the first time how to construct explicitly weak-basisinvariant constraints on the mass matrices, for a number of phenomenologicallyvalid mixing ansatze.

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