The Inverse Amplitude Method and Adler Zeros

Abstract

The Inverse Amplitude Method is a powerful unitarization technique to enlarge the energy applicability region of Effective Lagrangians. It has been widely used to describe resonances from Chiral Perturbation Theory as well as for the Strongly Interacting Symmetry Breaking Sector. In this work we show how it can be slightly modified to account also for the sub-threshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

17 pages, 4 figures

References in corpus (22)

• Meson-Meson interaction in a non-perturbative chiral approach
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• The inverse amplitude method in Chiral Perturbation Theory
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• A global fit of $\pi \pi$ and $\pi K$ elastic scattering in ChPT with dispersion relations
• Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
• The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations
• KK bar scattering amplitude to one loop in chiral perturbation theory, its unitarization and pion form factors
• Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length
• Proof of the Equivalence Theorem in the Chiral Lagrangian Formalism
• Thermal rho and sigma mesons from chiral symmetry and unitarity
• The Inverse Amplitude Method in $\pi \pi$ Scattering in Chiral Perturbation Theory to Two Loops
• LHC sensitivity to the resonance spectrum of a minimal strongly interacting electroweak symmetry breaking sector
• On the Equivalence Theorem in the $\chi PT$ Description of the Symmetry Breaking Sector of the Standard Model
• The Equivalence Theorem for Chiral Lagrangians
• Resonance Spectrum of the strongly interacting Symmetry Breaking Sector
• Improved Unitarized Heavy Baryon Chiral Perturbation Theory for $\pi N$ Scattering
• Pion scattering poles and chiral symmetry restoration
• Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory
• Improved Unitarized Heavy Baryon Chiral Perturbation Theory for pion-nucleon Scattering to fourth order
• The Inverse Amplitude Method and Heavy Baryon Chiral Perturbation Theory applied to pion-nucleon scattering
• Chiral Extrapolation of light resonances from Unitarized Chiral Perturbation Theory

Cited by in corpus (59)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• 50 Years of Quantum Chromodynamics
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• Resonances from meson-meson scattering in U(3) CHPT
• Towards a theory of hadron resonances
• Strange and non-strange quark mass dependence of elastic light resonances from SU(3) Unitarized Chiral Perturbation Theory to one loop
• Transport coefficients and resonances for a meson gas in Chiral Perturbation Theory
• Three-body unitarity versus finite-volume ${\pi }^{+}{\pi }^{+}{\pi }^{+}$ spectrum from lattice QCD
• Remarks on pole trajectories for resonances
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• Finite-volume energy spectrum of the $K^{-}{K}^{-}{K}^{-}$ system
• Dispersive analysis of the $\gamma {\gamma }^{\ast }\to \pi \pi$ process
• Three-body interactions from the finite-volume QCD spectrum
• The quark-mass dependence of elastic $\pi K$ scattering from QCD
• Multi-particle systems on the lattice and chiral extrapolations: a brief review
• Chiral Perturbation Theory, the $1/N_c$ expansion and Regge behaviour determine the structure of the lightest scalar meson
• A cross-channel study of pion scattering from lattice QCD
• Low-lying even parity meson resonances and spin-flavor symmetry
• Light "Higgs", yet strong interactions
• Pion scattering in the isospin I=2 channel from elongated lattices
• Connecting physical resonant amplitudes and lattice QCD
• Properties of the rho and sigma Mesons from Unitary Chiral Dynamics
• Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L{W}_L$, $Z_L{Z}_L$ and $hh$ scattering
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: The $\rho$-resonance
• The $\rho$-resonance with physical pion mass from $N_f=2$ lattice QCD
• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Chiral Extrapolations of the $\mathbf{\rho }(770)$ Meson in ${\mathbf{N}}_{\mathbf{f}}=2+1$ Lattice QCD Simulations
• Finite volume treatment of pi pi scattering and limits to phase shifts extraction from lattice QCD
• The $\gamma \pi \to \pi \pi$ anomaly from lattice QCD and dispersion relations
• Quark-mass dependence in $\omega \to 3\pi$ decays
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method
• Low-lying even parity meson resonances and spin-flavor symmetry revisited
• Singlet channel scattering in a Composite Higgs model on the lattice
• Two-Meson Form Factors in Unitarized Chiral Perturbation Theory
• Chiral Symmetry and light resonances in hot and dense matter
• Production cross section estimates for strongly-interacting Electroweak Symmetry Breaking Sector resonances at particle colliders
• From pole parameters to line shapes and branching ratios
• $\theta$-dependence of the lightest meson resonances in QCD
• The role of charged exotic states in $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$
• Chiral Extrapolation of the Sigma Resonance
• Fock space expansion of sigma meson in leading-Nc
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures
• Degeneracy patterns of chiral companions at finite temperature
• Analytical dispersive parameterization for elastic scattering of spinless particles
• The $\pi \pi$ scattering amplitude at large $N_{\text{c}}$
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance
• Advanced parametrisations for hadronic form factors
• Unitarity and Unitarization
• Pade Unitarizations: A Critical Look
• Pion scattering in finite volume within the Inverse Amplitude Method
• Chiral Extrapolation of light resonances from Unitarized Chiral Perturbation Theory
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$