2016/03/31 by Kristjan Kannike · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Bounded function #Computer science #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Excited state #Geometry #Higgs boson #Mathematical analysis #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #Quartic function #Scalar (mathematics) #Scalar potential #Singlet state #Stability (learning theory) #Theoretical physics #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-016-4160-3
published as Eur.Phys.J. C76 (2016) 324 · 24 pages, 5 figures, Mathematica notebook included in the source, 2HDM conditions corrected, simple numerical code for tensor eigenvalues added
openalex publication_date 2016/06/01 · arxiv created 2018/03/12 · arxiv updated 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We calculate analytical vacuum stability or bounded from below conditions for general scalar potentials of a few fields. After a brief review of copositivity, we show how to find positivity conditions for more complicated potentials. We discuss the vacuum stability conditions of the general potential of two real scalars, without and with the Higgs boson included in the potential. As further examples, we give explicit vacuum stability conditions for the two Higgs doublet model with no explicit CP breaking, and for the \mathbb Z3 scalar dark matter with an inert doublet and a complex singlet. We give a short overview of positivity conditions for tensors of quartic couplings via tensor eigenvalues.