Hilbert Series for Flavor Invariants of the Standard Model

TL;DR

This paper computes the Hilbert series for flavor invariants in the Standard Model, including neutrino and quark sectors, providing a mathematical framework to understand flavor symmetries and invariants.

Contribution

It introduces the calculation of Hilbert series for lepton and quark flavor invariants across different generations, extending previous analyses to include right-handed neutrinos.

Findings

Hilbert series for lepton flavor invariants with three generations including right-handed neutrinos.

Hilbert series for quark flavor invariants with four generations.

Provides a systematic method to analyze flavor invariants in the Standard Model.

Abstract

The Hilbert series is computed for the lepton flavor invariants of the Standard Model with three generations including the right-handed neutrino sector needed to generate light neutrino masses via the see-saw mechanism. We also compute the Hilbert series of the quark flavor invariants for the case of four generations.