Custodial symmetry, Georgi-Machacek model, and other scalar extensions

Abstract

In an SU(2) gauge theory, if the gauge bosons turn out to be degenerate after spontaneous symmetry breaking, obviously these mass terms are invariant under a global SU(2) symmetry that is unbroken. The pure gauge terms are also invariant under this symmetry. This symmetry is called the {\em custodial symmetry} (CS). In $\mathrm{SU}(2)\times \mathrm{U}(1)$ gauge theories, CS implies a mass relation between the $W$ and the $Z$ bosons. The Standard Model (SM), as well as various extensions of it in the scalar sector, possess such a symmetry. In this paper, we critically examine the notion of CS and show that there may be three different classes of CS, depending on the gauge couplings and self-couplings of the scalars. Among old models that preserve CS, we discuss the Two-Higgs Doublet Model and the one doublet plus two triplet model by Georgi and Machacek. We show that for two-triplet extensions, the Georgi-Machacek model is not the most general possibility with CS. Rather, we find, as the most general extension, a new model with more parameters and hence a richer phenomenology. Some of the consequences of this new model have also been discussed.

29 pages, 5 figures. Major changes in Section 2 regarding the classification of custodial symmetry. Version accepted in Physical Review D

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• Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U
• The decoupling limit in the Georgi-Machacek model
• Unitarity bounds in the Higgs model including triplet fields with custodial symmetry
• Search for charged Higgs bosons produced in vector boson fusion processes and decaying into vector boson pairs in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• Impact of Yukawa-like dimension-5 operators on the Georgi-Machacek model
• Accumulating Evidence for the Associated Production of a New Higgs Boson at the Large Hadron Collider

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• Democratic three Higgs-doublet models: the custodial limit and wrong-sign Yukawa
• Charged Higgs decay to $W^{\pm }$ and heavy neutral Higgs decaying into ${\tau }^{+}{\tau }^{-}$ in Georgi Machacek Model at LHC
• Positive definiteness constraints of effective scalar potential in Georgi-Machacek Model
• Tagging ultra-boosted jets at FCC-hh using machine learning techniques