Vacuum Stability Conditions for Higgs Potentials with $SU(2{)}_L$ Triplets

Abstract

Tree-level dynamical stability of scalar field potentials in renormalizable theories can in principle be expressed in terms of positivity conditions on quartic polynomial structures. However, these conditions cannot always be cast in a fully analytical resolved form, involving only the couplings and being valid for all field directions. In this paper we consider such forms in three physically motivated models involving $SU(2)$ triplet scalar fields: the Type-II seesaw model, the Georgi-Machacek model, and a generalized two-triplet model. A detailed analysis of the latter model allows to establish the full set of necessary and sufficient boundedness from below conditions. These can serve as a guide, together with unitarity and vacuum structure constraints, for consistent phenomenological (tree-level) studies. They also provide a seed for improved loop-level conditions, and encompass in particular the leading ones for the more specific Georgi-Machacek case. Incidentally, we present complete proofs of various properties and also derive general positivity conditions on quartic polynomials that are equivalent but much simpler than the ones used in the literature.

arXiv comment95 pages, 15 figures, 1 table, added comments in the introduction, 2 footnotes, a new paragraph in section V, new references, to appear in Physical Review D

References in corpus (36)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• The effective potential and the renormalisation group
• Vacuum Stability Conditions From Copositivity Criteria
• Minkowski space structure of the Higgs potential in 2HDM
• The Higgs Potential in the Type II Seesaw Model
• Stability and Symmetry Breaking in the General Two-Higgs-Doublet Model
• A search for a doubly-charged Higgs boson in pp collisions at sqrt(s) = 7 TeV
• Search for doubly charged Higgs boson production in multi-lepton final states with the ATLAS detector using proton-proton collisions at $\sqrt{s}$ = 13 TeV
• Vacuum Stability of a General Scalar Potential of a Few Fields
• The decoupling limit in the Georgi-Machacek model
• Improving the Effective Potential
• Consistency of the Two Higgs Doublet Model and CP violation in top production at the LHC
• Unitarity bounds in the Higgs model including triplet fields with custodial symmetry
• Displaced vertex signatures of doubly charged scalars in the type-II seesaw and its left-right extensions
• Consistency of the triplet seesaw model revisited
• Copositive Criteria and Boundedness of the Scalar Potential
• Doubly Charged Higgs Boson Production at Hadron Colliders
• Scalar phenomenology in type-II seesaw model
• Revisiting the high-scale validity of Type-II seesaw model with novel LHC signature
• Theoretical constraints on masses of heavy particles in Left-Right Symmetric Models
• Constraining a class of B-L extended models from vacuum stability and perturbativity
• Effects of custodial symmetry breaking in the Georgi-Machacek model at high energies
• Probing Doubly and Singly Charged Higgs at $pp$ Collider HE-LHC
• Stability and symmetry breaking in the general three-Higgs-doublet model
• Single-scale Renormalisation Group Improvement of Multi-scale Effective Potentials
• Reopen parameter regions in Two-Higgs Doublet Models
• Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials
• Vacuum Stability and Symmetry Breaking in Left-Right Symmetric Model
• Stability and symmetry breaking in the general n-Higgs-doublet model
• Perturbativity Constraints in BSM Models
• Doubly-charged Higgs Boson at Future Electron-Proton Collider
• Unitarity constraints in triplet extensions beyond the large s limit
• Theory and Phenomenology of Two Higgs Doublet Type-II Seesaw Model at the LHC Run-2
• Radiative Electroweak Symmetry Breaking in Standard Model Extensions
• The left-right supersymmetric option at a high-energy upgrade of the LHC

Cited by in corpus (16)

• Type II Seesaw Leptogenesis
• Unavoidable Higgs coupling deviations in the $Z_2$-symmetric Georgi-Machacek model
• Lepton Flavour Violation Tests of Type II Seesaw Leptogenesis
• More Constraints on the Georgi-Machacek Model
• Interpretation of 95 GeV Excess within the Georgi-Machacek Model in Light of Positive Definiteness Constraints
• The Type II Dirac Seesaw Portal to the mirror sector: Connecting neutrino masses and a solution to the strong CP problem
• Status of negative coupling modifiers for extended Higgs sectors
• Fermionic decay of charged Higgs boson in low mass region in Georgi Machacek Model
• Vacuum stability of the type II seesaw leptogenesis from inflation
• Interpretation of LHC excesses at 95 GeV and 152 GeV in an extended Georgi-Machacek model
• Origin of neutrino masses, dark matter, leptogenesis, and inflation in a seesaw model with triplets
• Triplet fermion WIMP dark matter in the general supersymmetric Georgi-Machacek model
• Boundedness from below of SU(n) potentials
• Vacuum Stability Conditions for New $SU(2)$ Multiplets
• Positive definiteness constraints of effective scalar potential in Georgi-Machacek Model
• Accidental symmetries in the scalar potential of the Standard Model extended with two Higgs triplets