Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data

Abstract

We investigate the determination of the $\sigma$ pole from $\pi \pi$ scattering data below the $K\bar{K}$ threshold, including the new precise results obtained from $K_{e4}$ decay by NA48/2 Collaboration. We discuss also the experimental status of the threshold parameters $a_0^0$ and $b_0^0$ and the phase shift ${\delta }_0^0$. In order to reduce the theoretical bias, we use a large class of analytic parametrizations of the isoscalar $S$-wave, based on expansions in powers of conformal variables. The $\sigma$ pole obtained with this method is consistent with the prediction based on ChPT and Roy equations. However, the theoretical uncertainties are now larger, reflecting the sensitivity of the pole position to the specific parametrizations valid in the physical region. We conclude that Roy equations offer the most precise method for the determination of the $\sigma$ pole from $\pi \pi$ elastic scattering.

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Cited by in corpus (38)

• 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
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• Regge analysis of the pi pi scattering amplitude
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Lattice study of light scalar tetraquarks with I=0,2,1/2,3/2: are sigma and kappa tetraquarks?
• On the size of the sigma meson and its nature
• Extraction of isoscalar $\pi \pi$ phase-shifts from lattice QCD
• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• The pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV
• No classical limit of quantum decay for broad states
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Distinguishing two kinds of scalar mesons from heavy meson decays
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Strange resonance poles from $K\pi$ scattering below 1.8 GeV
• Padé Approximants and Resonance Poles
• The analytical $\pi \pi$ scattering amplitude and the light scalars
• Serber symmetry, Large Nc and Yukawa-like One Boson Exchange Potentials
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• On the uncertainty estimates of the $\sigma$-pole determination by Padé approximants
• Nature of the sigma meson as revealed by its softening process
• Meson Resonances at large Nc: Complex Poles vs Breit-Wigner Masses
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Preliminary lattice study of $\sigma$ meson decay width
• Modified $\pi \pi$ amplitude with $\sigma$ pole
• Parameters of scalar resonances from the combined analysis of data on processes $\pi \pi \to \pi \pi ,K\bar{K},\eta \eta$ and $J/\psi$ decays
• The $\pi f_0(500)$ decay of the $a_1(1260)$
• Pion scalar form factor and model independent values of $f_0(500)$ and $f_0(980)$ meson parameters
• P-wave pi pi amplitude from dispersion relations
• Analytical dispersive parameterization for elastic scattering of spinless particles
• On the low energy end of the QCD spectrum
• On concise hypotheses for the interpretation of a wide scalar resonance as gauge boson binary in QCD - some new analyses
• Scalar mesons in eta' -> eta pi0 pi0 decay
• Assessing the role of threshold conditions in the determination of uncertainties in pole extractions using Padé approximants
• Dispersive determination of resonances from $\pi \pi$ scattering data
• Scalar mesons in ${\eta }^{\prime }\to 3{\pi }^0,{\pi }^0{\pi }^{+}{\pi }^{-}$ decays
• Low-energy QCD and hadronic structure
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$