Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L{W}_L$, $Z_L{Z}_L$ and $hh$ scattering

Abstract

If the Electroweak Symmetry Breaking Sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity (where the perturbative expansion breaks down). This is achieved by dispersion relations, whose subtraction constants and left cut contribution can be approximately obtained in different ways giving rise to different unitarization procedures. We illustrate the ideas with the Inverse Amplitude Method, one version of the N/D method and another improved version of the K-matrix. In the three cases we get partial waves which are unitary, analytical with the proper left and right cuts and in some cases poles in the second Riemann sheet that can be understood as dynamically generated resonances. In addition they reproduce at Next to Leading Order (NLO) the perturbative expansion for the five partial waves not vanishing (up to J=2) and they are renormalization scale ($\mu$) independent. Also the unitarization formalisms are extended to the coupled channel case. Then we apply the results to the elastic scattering amplitude for the longitudinal components of the gauge bosons $V=W,Z$ at high energy. We also compute $hh\to hh$ and the inelastic process $VV\to hh$ which are coupled to the elastic $VV$ channel for custodial isospin $I=0$. We numerically compare the three methods for various values of the low-energy couplings and explain the reasons for the differences found in the $I=J=1$ partial wave. Then we study the resonances appearing in the different elastic and coupled channels in terms of the effective Lagrangian parameters.

arXiv comment45 pages, 28 figures

References in corpus (48)

• 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
• FeynRules 2.0 - A complete toolbox for tree-level phenomenology
• Automatized One-Loop Calculations in 4 and D dimensions
• The Minimal Composite Higgs Model
• The Strongly-Interacting Light Higgs
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Light custodians in natural composite Higgs models
• FORM version 4.0
• Phenomenology of the Little Higgs Model
• Physics Interplay of the LHC and the ILC
• Light scalar at LHC: the Higgs or the dilaton?
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• The inverse amplitude method in Chiral Perturbation Theory
• Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
• The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
• Global fit to Higgs signal strengths and couplings and implications for extended Higgs sectors
• Effective Field Theory: A Modern Approach to Anomalous Couplings
• Model-Independent Bounds on a Light Higgs
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• WW scattering at the LHC
• The universal Higgs fit
• On the effect of resonances in composite Higgs phenomenology
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• Disentangling a dynamical Higgs
• Updated Global Analysis of Higgs Couplings
• LHC Analysis of the Strongly Interacting $WW$ System: Gold-Plated Modes
• Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO
• The Inverse Amplitude Method and Adler Zeros
• One-loop $W_L{W}_L$ and $Z_L{Z}_L$ scattering from the Electroweak Chiral Lagrangian with a light Higgs-like scalar
• Longitudinal WW scattering in light of the "Higgs" discovery
• Search for long-lived, multi-charged particles in pp collisions at sqrt(s)=7 TeV using the ATLAS detector
• LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector
• Radiative corrections to WL WL scattering in composite Higgs models
• On the Equivalence Theorem in the $\chi PT$ Description of the Symmetry Breaking Sector of the Standard Model
• Light "Higgs", yet strong interactions
• The Case of a WW Dynamical Scalar Resonance within a Chiral Effective Description of the Strongly Interacting Higgs Sector
• The Equivalence Theorem for Chiral Lagrangians
• On the renormalization of the electroweak chiral Lagrangian with a Higgs
• Search for heavy vector-like quarks coupling to light quarks in proton-proton collisions at sqrt(s) = 7 TeV with the ATLAS detector
• Unitarity and causality constraints in composite Higgs models
• Chiral Perturbation Theory and the f2(1270) resonance
• RENORMALIZATION and the EQUIVALENCE THEOREM: ON-SHELL SCHEME
• The 4-Dimensional Composite Higgs Model (4DCHM) and the 125 GeV Higgs-like signals at the LHC
• The Use of Dispersion Relations in the $\pi \pi$ and $K\bar{K}$ Coupled-Channel System
• Strongly Coupled Models with a Higgs-like Boson
• Higgs Physics in the Large N limit
• Unitarity-controlled resonances after Higgs discovery

Cited by in corpus (27)

• The Standard Model as an Effective Field Theory
• Studies of Dimension-Six EFT effects in Vector Boson Scattering
• The flair of Higgsflare: Distinguishing electroweak EFTs with $W_L{W}_L\to n\times h$
• Resonances at the LHC beyond the Higgs: The Scalar/Tensor Case
• Unitarization effects in EFT predictions of WZ scattering at the LHC
• Possible new resonance from $W_L{W}_L$-$hh$ interchannel coupling
• Inverse Amplitude Method for Perturbative Electroweak Symmetry Breaking Sector: The Singlet Higgs Portal as a Study Case
• Production of vector resonances at the LHC via WZ-scattering: a unitarized EChL analysis
• Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method
• Strongly coupled theories beyond the Standard Model
• Axion-Higgs interplay in the two Higgs-doublet model
• Vector boson scattering at the LHC. A study of the WW -> WW channels with the Warsaw cut
• Introducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT
• Testing anomalous $H-W$ couplings and Higgs self-couplings via double and triple Higgs production at $e^{+}{e}^{-}$ colliders
• Colorful Imprints of Heavy States in the Electroweak Effective Theory
• Higgs-Electroweak Chiral Lagrangian: One-Loop Renormalization Group Equations
• The role of the thermal $f_0(500)$ in chiral symmetry restoration
• Coupling WW, ZZ unitarized amplitudes to $\gamma \gamma$ in the TeV region
• Production cross section estimates for strongly-interacting Electroweak Symmetry Breaking Sector resonances at particle colliders
• Top-antitop production from $W_L^{+}{W}_L^{-}$ and $Z_L{Z}_L$ scattering under a strongly-interacting symmetry-breaking sector
• Interpreting a 2 TeV resonance in WW scattering
• Glueball-glueball scattering and the glueballonium
• Perturbative Higgs CP violation, unitarity and phenomenology
• Implications of Vector Boson Scattering Unitarity in Composite Higgs Models
• Seeking for resonances in unitarized one-loop graviton-graviton scattering
• Unitarity and Unitarization
• Coupling of $t\bar{t}$ and $\gamma \gamma$ with a strongly interacting Electroweak Symmetry Breaking Sector