Invariants, Alignment and the Pattern of Fermion Masses and Mixing

Abstract

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 an approximate tribimaximal lepton mixing matrix. We also show the usefulness of these invariants in the study of specific ans\"atze for the flavour structure of fermion mass matrices.