Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm

Abstract

We show how complex resonance poles and threshold energies for systems in hadron physics can be accurately obtained by using a method based on the Padé-approximant which was recently developed for the calculation of resonance poles for atomic and molecular auto-ionization systems. The main advantage of this method is the ability to calculate the resonance poles and threshold energies from \emph{real} spectral data. In order to demonstrate the capabilities of this method we apply it here to an analytical model as well as to experimental data for the squared modulus of the vector pion form factor, the S0 partial wave amplitude for $\pi \pi$ scattering and the cross section ratio $R(s)$ for $e^{+}{e}^{-}$ collisions. The extracted values for the resonance poles of the $\rho (770)$ and the $f_0(500)$ or $\sigma$ meson are in very good agreement with the literature. When the data are noisy the prediction of decay thresholds proves to be less accurate but feasible.

6 pages, 4 figures

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• Big-Bang Nucleosynthesis
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Probabilistic interpretation of compositeness relation for resonances
• Flow equations for spectral functions at finite external momenta
• Atomic and molecular complex resonances from real eigenvalues using standard (hermitian) electronic structure calculations
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• Diquark Correlations in Hadron Physics: Origin, Impact and Evidence
• Spectral functions of confined particles
• Symmetry, symmetry breaking, and pion parton distributions
• Empirical Consequences of Emergent Mass
• Numerical analytic continuation of Euclidean data
• Impressions of the Continuum Bound State Problem in QCD
• Static quark anti-quark interactions at non-zero temperature from lattice QCD
• Elastic electromagnetic form factors of vector mesons
• Nucleon-to-Roper electromagnetic transition form factors at large-$Q^2$
• Drawing insights from pion parton distributions
• Novel approaches in Hadron Spectroscopy
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• Fresh extraction of the proton charge radius from electron 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 $K_0^{\ast }(700)$
• Scattering amplitudes and contour deformations
• Bound state properties from the Functional Renormalisation Group
• Four-quark states from functional methods
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• The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach
• Pion charge radius from pion+electron elastic scattering data
• Going to the light front with contour deformations
• Hadron and light nucleus radii from electron scattering
• Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets
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• The f0(1370) controversy from dispersive meson-meson scattering data analyses
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• Thermal properties of $\pi$ and $\rho$ meson
• Pauli radius of the proton
• Fresh look at experimental evidence for odderon exchange
• Gravitational form factors of the proton from near-threshold vector meson photoproduction
• Finite temperature sum rules in the vector channel at finite momentum
• Static quark anti-quark interactions at non-zero temperature from lattice QCD
• Extracting a model quark propagator's spectral density
• Padé Approximants and the analytic structure of the gluon and ghost propagators
• Dispersive determination of resonances from $\pi \pi$ scattering data
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• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$