Symmetry and geometry in generalized Higgs effective field theory -- Finiteness of oblique corrections v.s. perturbative unitarity

Abstract

We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters S and U can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands the flatness of the scalar manifold. The relationship between the finiteness of the electroweak oblique corrections and perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, then the one-loop finiteness of the oblique correction parameters S and U is automatically guaranteed.

arXiv comment55 pages; an appendix on symmetry-geometry dictionary added; version accepted for publication in PRD

References in corpus (90)

• 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
• Theory and phenomenology of two-Higgs-doublet models
• Dimension-Six Terms in the Standard Model Lagrangian
• The Minimal Composite Higgs Model
• The Strongly-Interacting Light Higgs
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Higgs as a Holographic Pseudo-Goldstone Boson
• Effective Lagrangian for a light Higgs-like scalar
• Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
• The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
• Updated Global SMEFT Fit to Higgs, Diboson and Electroweak Data
• Global fit to Higgs signal strengths and couplings and implications for extended Higgs sectors
• Model-Independent Bounds on a Light Higgs
• The Other Natural Two Higgs Doublet Model
• The Chiral Approach to the Electroweak Interactions
• A Higgs-Higgs bound state due to New Physics at a TeV
• Higgs windows to new physics through d = 6 operators: Constraints and one-loop anomalous dimensions
• Robust Determination of the Higgs Couplings: Power to the Data
• Complete Higgs Sector Constraints on Dimension-6 Operators
• Constraining anomalous Higgs interactions
• The Electroweak Chiral Lagrangian and New Precision Measurements
• Curing the Ills of Higgsless Models: the S Parameter and Unitarity
• Model-independent precision constraints on dimension-6 operators
• Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)
• On the Validity of the Effective Field Theory Approach to SM Precision Tests
• Anomalous Higgs Boson Production and Decay
• A Geometric Formulation of Higgs Effective Field Theory: Measuring the Curvature of Scalar Field Space
• Geometry of the Scalar Sector
• Effects of genuine dimension-six Higgs operators
• On the Power Counting in Effective Field Theories
• Renormalization of dimension-six operators relevant for the Higgs decays $h\to \gamma \gamma ,\gamma Z$
• LHC constraints on two-Higgs doublet models
• Probing wrong-sign Yukawa couplings at the LHC and a future linear collider
• Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO
• A Three Site Higgsless Model
• Determining Triple Gauge Boson Couplings from Higgs Data
• Fingerprinting non-minimal Higgs sectors
• Resonances and Unitarity in Weak Boson Scattering at the LHC
• A Closed Formula for the Riemann Normal Coordinate Expansion
• Higgs boson pair production in non-linear Effective Field Theory with full $m_t$-dependence at NLO QCD
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• Effects of Fermion Localization in Higgsless Theories and Electroweak Constraints
• A Higgs or Not a Higgs? What to Do if You Discover a New Scalar Particle
• Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian
• Heavy Higgs Searches and Constraints on Two Higgs Doublet Models
• Measuring extended Higgs sectors as a consistent free couplings model
• Ideal Fermion Delocalization in Higgsless Models
• Carving Out Parameter Space in Type-II Two Higgs Doublets Model
• Exploring Two Higgs Doublet Models Through Higgs Production
• Low-Energy Constraints on New Physics Revisited
• On Gauge Invariance and Minimal Coupling
• Exclusive Signals of an Extended Higgs Sector
• Renormalization group evolution of Higgs effective field theory
• Top and Bottom: a Brane of Their Own
• Playing with fermion couplings in Higgsless models
• Mass-degenerate Higgs bosons at 125 GeV in the Two-Higgs-Doublet Model
• Comprehensive study of two Higgs doublet model in light of the new boson with mass around 125 GeV
• Proof of the Equivalence Theorem in the Chiral Lagrangian Formalism
• Fitting Higgs Data with Nonlinear Effective Theory
• Deconstructed Higgsless Models with One-Site Delocalization
• Constraining parameter space in type-II two-Higgs doublet model in light of a 126 GeV Higgs boson
• Higgs boson signal at complete tree level in the SM extension by dimension-six operators
• WW Scattering in the Era of Post Higgs Discovery
• Testing anomalous gauge couplings of the Higgs boson via weak-boson scatterings at the LHC
• One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs
• The Electroweak Chiral Lagrangian and CP-Violating Effects in Technicolor Theories
• Chiral Perturbation to One Loop Including the $\rho$ Meson
• One-loop Renormalization of Resonance Chiral Theory: Scalar and Pseudoscalar Resonances
• Asymptotic safety and the gauged SU(N) nonlinear sigma-model
• The 2HDM-X and Large Hadron Collider Data
• An Effective Higgsless Theory: Satisfying Electroweak Constraints and a Heavy Top Quark
• Unitarity sum rules, three site moose model, and the ATLAS 2 TeV diboson anomalies
• Effects of the anomalous Higgs couplings on the Higgs boson production at the Large Hadron Collider
• General Sum Rules for WW Scattering in Higgsless Models: Equivalence Theorem and Deconstruction Identities
• Power-counting and Renormalizability in Lifshitz Scalar Theory
• Implications on the Heavy CP-even Higgs Boson from Current Higgs Data
• Does the three site Higgsless model survive the electroweak precision tests at loop?
• Supersymmetry versus Compositeness: 2HDMs tell the story
• A Concrete Composite 2-Higgs Doublet Model
• Tree-Level Unitarity and Renormalizability in Lifshitz Scalar Theory
• Effective Field Theory of Precision Electroweak Physics at One Loop
• Determination of tan(beta) from the Higgs boson decay at linear colliders
• S-matrix Unitarity and Renormalizability in Higher Derivative Theories
• The Flavor Structure of the Three-Site Higgsless Model
• Matter scattering in $R_{\mu \nu }^2$ gravity and unitarity
• Does unitarity imply finiteness of electroweak oblique corrections at one-loop? - constraining extra neutral Higgs bosons -
• Classification of simple heavy vector triplet models

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