Study of weak-basis invariants in the universal seesaw model using Hilbert series

TL;DR

This paper applies Hilbert Series techniques to analyze weak-basis invariants within the Universal Seesaw Model, focusing on a one-generation quark sector to understand mass hierarchy and invariant structures.

Contribution

It introduces a novel application of Hilbert Series to study weak-basis invariants in the Universal Seesaw Model, specifically for the one-generation case.

Findings

Hilbert Series effectively characterizes weak-basis invariants.

The approach clarifies invariant structures related to quark mass hierarchy.

Provides a framework for extending analysis to multi-generation cases.

Abstract

Universal Seesaw Model is a model which explains the mass hierarchy of the quark sector. This model introduces vector-like quarks. The top quark mass is generated in the electroweak scale and the other quark mass is generated using a seesaw-like mechanism. The invariant theory helps construct a weak-basis invariant. We study the weak-basis invariant (WBI) using Hilbert Series (HS) and apply it to the Universal Seesaw Model, particularly the one-generation case of the quark sector.