Experimental status of the $\pi \pi$ isoscalar S wave at low energy: $f_0(600)$ pole and scattering length

Abstract

The experimental results obtained in the last few years on kaon decays (K$\to 2\pi$ and, above all, Ke4 decays) allow a reliable, model independent determination of low energy $\pi \pi$ scattering in the S0 wave. Using them and, eventually, other sets of data, it is possible to give a precise parametrization of the S0 wave as well as to find the scattering length and effective range parameter. One can also perform an extrapolation to the pole of the "$\sigma$ resonance" [$f_0(600)$]. We obtain the results $$a_0^{(0)}=0.233\pm 0.013M_{\pi }^{-1},b_0^{(0)}=0.285\pm 0.012M_{\pi }^{-3}$$ and, for the $\sigma$ pole, $$M_σ=484\pm17 \mev,\quad\gammav_σ/2= 255\pm10 {\rm MeV}.$$

arXiv commentPlain TeX;4 figures; improved data used; version to appear in Phys. Rev. D

References in corpus (23)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• ππscattering
• Meson-Meson interaction in a non-perturbative chiral approach
• Mass and width of the lowest resonance in QCD
• The inverse amplitude method in Chiral Perturbation Theory
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• A new measurement of K+(e4) decay and the s-wave pi-pi-scattering length a00
• The hadronic contributions to the anomalous magnetic moment of the muon
• Study of the Decay phi --> pi0 pi0 gamma with the KLOE Detector
• The pion-pion scattering amplitude
• Light scalars as tetraquarks or two-meson states from large Nc and unitarized Chiral Perturbation Theory
• Determination of the a0-a2 pion scattering length from K->pi+ pi0 pi0 decay
• Precision Determination of the Pion Form Factor and Calculation of the Muon $g-2$
• First measurement of the ${\pi }^{+}{\pi }^{-}$ atom lifetime
• Pion-pion scattering and the K->3pi decay amplitudes
• Observation of a cusp-like structure in the pizero-pizero invariant mass distribution from K+- ==> pi+- pizero pizero decay and determination of the pi-pi scattering lengths
• Analysis and interpretation of new low-energy Pi-Pi scattering data
• Isospin Breaking in K -> Pi Pi Decays
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• Regge analysis of pion-pion (and pion-kaon) scattering for energy s^{1/2}>1.4 GeV
• On the precision of chiral-dispersive calculations of $\pi \pi$ scattering
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering
• The scalar radius of the pion

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