Invariants, alignment and the pattern of fermion masses and mixing

We show that the main features of the pattern of fermion masses and mixing can be expressed in terms of simple relations among weak-basis invariants. In the quark sector, we identify the weak-basis invariants which signal the observed alignment of the up and down quark mass matrices in flavour space. In the lepton sector, we indicate how a set of conditions on weak-basis invariants can lead to the observed pattern of leptonic mixing, including the recent measurement of U-e3 by the Daya Bay Collaboration. We also show the usefulness of these invariants in the study of specific ansatze for the flavour structure of fermion mass matrices. (c) 2012 Elsevier B.V. All rights reserved.