The Hilbert Series and the Flavor Invariants of the 3HDM

TL;DR

This paper systematically analyzes the invariant operators in the three-Higgs-doublet model by computing the Hilbert series and explicitly constructing invariants up to cubic order.

Contribution

It provides the first detailed computation of the Hilbert series and explicit invariants for the 3HDM's global symmetry group.

Findings

Computed the Hilbert series for the 3HDM

Constructed explicit invariants up to cubic order

Enhanced understanding of the model's symmetry structure

Abstract

We perform a systematic study of invariant operators in the three-Higgs-doublet model (3HDM). We compute the Hilbert series associated with the global symmetry group of the theory. In addition, we construct explicit expressions for these invariants up to cubic order in the couplings.