Symmetry and decoupling in multi Higgs models

TL;DR

This paper investigates the conditions under which multi Higgs doublet models exhibit decoupling, demonstrating that symmetry in the vacuum state is both necessary and sufficient for decoupling to occur.

Contribution

It provides a general proof linking vacuum symmetry to decoupling in multi Higgs models and analyzes specific cases for three Higgs doublets.

Findings

Decoupling occurs if and only if the vacuum preserves the symmetry.

Explicit analysis of three Higgs doublet models confirms the general result.

Different decoupling patterns have characteristic features.

Abstract

We study the scalar sector of the most general multi Higgs doublet model satisfying explicitly an exact symmetry. We prove that such a model will exhibit decoupling if and only if the vacuum also satisfies the same symmetry. This general property is also shown independently and explicitly for three Higgs doublet models, by considering in detail all symmetry-constrained models and their possible vacua. We also discuss some specific characteristics of different decoupling patterns.