Invariants, Alignment and the Pattern of Fermion Masses and Mixing

TL;DR

This paper demonstrates how fermion mass and mixing patterns can be characterized by weak-basis invariants, providing insights into quark and lepton flavor structures and their alignments.

Contribution

It introduces the use of weak-basis invariants to analyze fermion mass matrices and mixing patterns, including quark alignment and lepton tribimaximal mixing.

Findings

Weak-basis invariants signal quark mass matrix alignment.

Conditions on invariants lead to tribimaximal lepton mixing.

Invariants assist in analyzing fermion flavor ansätze.

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.