Unitarity and Unitarization

Abstract

This article reviews unitarization methods essential for extending Effective Field Theories (EFTs) beyond their perturbative limits, particularly in hadronic and electroweak (EW) sectors. Perturbative EFTs, like Chiral Perturbation Theory (ChPT), often violate unitarity bounds at higher energies, a breakdown observed in phenomena such as $\pi \pi$ scattering resonances. To overcome this, non-perturbative techniques including the Inverse Amplitude Method (IAM), $K$-matrix formalism, and N/D approach are detailed. The IAM and the N/D methods resum perturbative series while preserving fundamental $S$-matrix principles: unitarity, analyticity, and causality, dynamically generating resonant behavior. The article emphasizes the unique role of dispersive frameworks, especially the Roy equations, which rigorously incorporate analyticity and crossing symmetry. It highlights their potential for future application in the electroweak sector, offering a powerful tool to constrain the Standard Model and interpret collider data.

References in corpus (37)

• ππscattering
• Mass and width of the lowest resonance in QCD
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Roy equation analysis of pi pi scattering
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Roy-Steiner-equation analysis of pion-nucleon scattering
• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
• The K^*_0(800) scalar resonance from Roy-Steiner representations of pi K scattering
• The pi pi S-wave scattering lengths
• Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
• Analysis of General Power Counting Rules in Effective Field Theory
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• Precision tests of fundamental physics with $\eta$ and ${\eta }^{\prime }$ mesons
• The $\kappa$ resonance in s wave $\pi K$ scatterings
• The Inverse Amplitude Method and Adler Zeros
• Three-body Unitarity with Isobars Revisited
• High-Energy Vector Boson Scattering after the Higgs Discovery
• An improved study of the kappa resonance and the non-exotic $s$ wave $\pi K$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data
• Improved dispersion relations for γγ\to π^0π^0
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• Light "Higgs", yet strong interactions
• Partial waves and large $N_C$ resonance sum rules
• Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L{W}_L$, $Z_L{Z}_L$ and $hh$ scattering
• Physics of the Analytic S-Matrix
• Possible new resonance from $W_L{W}_L$-$hh$ interchannel coupling
• Three-body scattering: Ladders and Resonances
• Some Remarks on the Pade Unitarization of Low-Energy Amplitudes
• Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method
• The [1,2] Padé Amplitudes for $\pi \pi$ Scatterings in Chiral Perturbation Theory
• The Constraints of Unitary on $\pi \pi$ Scattering Dispersion Relations
• Coupling WW, ZZ unitarized amplitudes to $\gamma \gamma$ in the TeV region
• Global parametrizations of $\pi \pi$ scattering with dispersive constraints: Beyond the S0 wave
• Crossing Symmetry Violation of Unitarized Pion-Pion Amplitude in the Resonance Region
• Is the $\sigma$ meson dynamically generated?