The invariant space of multi-Higgs doublet models

Abstract

In a model with more than one scalar doublet, the parameter space encloses both physical and unphysical information. Invariant theory provides a detailed description of the counting and characterization of the physical parameter space. The Hilbert series for the 3HDM is computed for the first time using partition analysis, in particular Omega calculus, giving rise to the possibility of a full description of its physical parameters. A rigorous counting of the physical parameters is given for the full class of models with $N$ scalar doublets as well as a decomposition of the Lagrangian into irreducible representations of $\mathrm{SU}(N)$. For the first time we derive a basis-invariant technique for counting parameters in a Lagrangian with both basis-invariant redundancies and global symmetries.

arXiv commentAdded references. Conjecture now a theorem. Added details

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Cited by in corpus (6)

• Flavor Invariants and Renormalization-group Equations in the Leptonic Sector with Massive Majorana Neutrinos
• Beyond Jarlskog: 699 invariants for CP violation in SMEFT
• CP violation and flavor invariants in the seesaw effective field theory
• Assessing boundedness from below in the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric three-Higgs-doublet model: algorithm and machine learning
• The Hilbert Series and the Flavor Invariants of the 3HDM
• Flavour Invariants of the N Higgs Doublet Model