Model independent determination of the sigma pole

Abstract

The first part of this report reviews recent developments at the interface between lattice work on QCD with light dynamical quarks, effective field theory and low energy precision experiments. Then I discuss how dispersion theory can be used to analyze the low energy structure of the $\pi \pi$ scattering amplitude in a model independent manner. This leads to an exact formula for the mass and width of the lowest few resonances, in terms of observable quantities. As an application, I consider the pole position of the $\sigma$, paying particular to error propagation in the numerical analysis. The report is based on work done in collaboration with Irinel Caprini and Gilberto Colangelo.

10 pages, 4 figures, Contribution to the proceedings of the Workshop on Scalar Mesons and Related Topics, honouring the 70th birthday of Michael Scadron, Lisbon, Portugal, Feb. 11-16, 2008

References in corpus (5)

• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Quark mass dependence of the rho and sigma from dispersion relations and Chiral Perturbation Theory
• Identification of a Scalar Glueball
• Theoretical progress on cusp effect and Kl4 decays
• Theoretical progress on pi pi scattering lengths and phases

Cited by in corpus (29)

• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• Hadron properties in the nuclear medium
• Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis
• 50 Years of Quantum Chromodynamics
• Meson vacuum phenomenology in a three-flavor linear sigma model with (axial-)vector mesons
• Regge analysis of the pi pi scattering amplitude
• Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance
• Chiral extrapolation of light resonances from one and two-loop unitarized Chiral Perturbation Theory versus lattice results
• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• No classical limit of quantum decay for broad states
• Large-Nc Properties of the rho and f0(600) Mesons from Unitary Resonance Chiral Dynamics
• Finding the sigma pole by analytic extrapolation of $\pi \pi$ scattering data
• Phenomenology of charmed mesons in the extended Linear Sigma Model
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Some Remarks on the Pade Unitarization of Low-Energy Amplitudes
• Serber symmetry, Large Nc and Yukawa-like One Boson Exchange Potentials
• Data-driven dispersive analysis of the $\pi \pi$ and $\pi K$ scattering
• Chiral effective theory with a light scalar and lattice QCD
• The role of the next-to-leading order triangle-shaped diagram in two-body hadronic decays
• Di-Electrons from Resonances in Nucleon-Nucleon Collisions
• On the $\pi \pi$ contribution to the QCD sum rules for the light tetraquark
• Gravitons and Pions
• Analytical dispersive parameterization for elastic scattering of spinless particles
• On concise hypotheses for the interpretation of a wide scalar resonance as gauge boson binary in QCD - some new analyses
• On the low energy end of the QCD spectrum
• Improvement of multichannel amplitudes for the pion-pion scattering using the dispersion relations
• Influence of Vector Mesons on the f0(600) Decay Width in a Linear Sigma Model with Global Chiral Invariance
• Low Energy Constants of Chiral Perturbation Theory from the Instanton Vacuum
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$