Structure of potentials with $N$ Higgs doublets

TL;DR

This paper explores the mathematical structure of N-Higgs-doublet models, revealing a Minkowski space framework that helps analyze potential stability, minima, and vacuum types in extended Standard Model scenarios.

Contribution

It introduces a Minkowski space parametrization for N-Higgs-doublet models, enabling new insights into potential boundedness, minima classification, and vacuum structure.

Findings

Minkowski structure emerges in variable and parameter spaces.

Parametrization in terms of lightlike vectors with specific angular relations.

Conditions for potential boundedness and minima characterization.

Abstract

Extensions of the Standard Model with $N$ Higgs doublets are simple extensions presenting a rich mathematical structure. An underlying Minkowski structure emerges from the study of both variable space and parameter space. The former can be completely parametrized in terms of two future lightlike Minkowski vectors with spatial parts forming an angle whose cosine is $-(N-1)^{-1}$. For the parameter space, the Minkowski parametrization enables one to impose sufficient conditions for bounded below potentials, characterize certain classes of local minima and distinguish charge breaking vacua from neutral vacua. A particular class of neutral minima presents a degenerate mass spectrum for the physical charged Higgs bosons.