Yet another lesson on the stability conditions in multi-Higgs potentials

A bstract We discuss a rather common but often unnoticed pitfall which arises when deriving the bounded-from-below (BFB) conditions in multi-Higgs models with softly broken global symmetries. Namely, necessary and sufficient BFB conditions derived for the case with an exact symmetry can be ruined by...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2020; no. 11; pp. 1 - 28
Main Authors Ivanov, Igor P., Vazão, Francisco
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020
Springer Nature B.V
SpringerOpen
Subjects
Beyond Standard Model
Broken symmetry
Classical and Quantum Gravitation
Elementary Particles
Global Symmetries
Higgs Physics
High energy physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Symmetry
Global Symmetries
Beyond Standard Model
Higgs Physics
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Summary:A bstract We discuss a rather common but often unnoticed pitfall which arises when deriving the bounded-from-below (BFB) conditions in multi-Higgs models with softly broken global symmetries. Namely, necessary and sufficient BFB conditions derived for the case with an exact symmetry can be ruined by introducing soft symmetry breaking terms. Using S 4 and A 4 -symmetric three-Higgs-doublet models as an example, we argue that all published necessary and sufficient BFB conditions, even those which are correct for the exactly symmetric case, are no longer sufficient if soft symmetry breaking is added. Using the geometric formalism, we derive the exact necessary and sufficient BFB conditions for the 3HDM with the symmetry group S 4 , either exact or softly broken, and review the situation for the A 4 -symmetric case.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2020)104