Algebraic Structure of Lepton and Quark Flavor Invariants and CP Violation

TL;DR

This paper analyzes the algebraic structure of flavor invariants in lepton and quark sectors, exploring their relations, classification, and implications for CP violation within the Standard Model and seesaw models.

Contribution

It provides a detailed classification of flavor invariants and computes the Hilbert series, offering new algebraic insights into CP violation and flavor symmetry.

Findings

The invariant ring in the lepton sector is highly non-trivial.

Classification of invariants for two and three generations is achieved.

An invariant definition of the CP-violating angle theta is provided.

Abstract

Lepton and quark flavor invariants are studied, both in the Standard Model with a dimension five Majorana neutrino mass operator, and in the seesaw model. The ring of invariants in the lepton sector is highly non-trivial, with non-linear relations among the basic invariants. The invariants are classified for the Standard Model with two and three generations, and for the seesaw model with two generations, and the Hilbert series is computed. The seesaw model with three generations proved computationally too difficult for a complete solution. We give an invariant definition of the CP-violating angle theta in the electroweak sector.