Representation-theoretical characterization of canonical custodial symmetry in NHDM potentials

Abstract

By considering the basis-covariant constituents of N-Higgs-doublet potentials, we derive necessary and sufficient conditions for canonical SO(4)_C Custodial Symmetry (CS) of potentials with N>2 doublets, based on representation-theoretical and geometrical relations. In essence, our characterization relates the presence of canonical CS to basis-covariant vectors corresponding to particular bases of the defining representation of the orthogonal Lie algebras. For N=3,4 and 5, the conditions demand little computational effort to be evaluated, and we provide practical algorithms that may be efficiently implemented in a computer program, for deciding whether or not a potential is custodial-symmetric.

arXiv comment26 pages, the proof of Theorem 1 is modified so the theorem also is valid for the case N=8

References in corpus (21)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U
• A Twisted Custodial Symmetry in the Two-Higgs-Doublet Model
• Vacuum Topology of the Two Higgs Doublet Model
• CP violation conditions in N-Higgs-doublet potentials
• CP Violation in the General Two-Higgs-Doublet Model: a Geometric View
• LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory
• Constraints on CP violation in the Higgs sector from the $\rho$ parameter
• On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential
• Note on Custodial Symmetry in the Two-Higgs-Doublet Model
• Classifying Accidental Symmetries in Multi-Higgs Doublet Models
• Recognizing symmetries in 3HDM in basis-independent way
• Symmetry and Mass Degeneration in Multi-Higgs-Doublet Models
• Stability and symmetry breaking in the general n-Higgs-doublet model
• Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials
• Basis-invariant conditions for CP symmetry of order 4
• Multi-Higgs models with CP symmetries of increasingly high order
• Symmetries for the 4HDM: extensions of cyclic groups
• On the terms violating the custodial symmetry in multi-Higgs-doublet models
• Lepton Flavor Specific Extended Higgs Model
• Impacts of multi-Higgs on the $\rho$ parameter, decays of a neutral Higgs to $WW$ and $ZZ$, and a charged Higgs to $WZ$