Analytical $\pi \pi$ scattering amplitude and the light scalars-II

Abstract

In the paper Phys. Rev. {\bf D83}, 054008 (2011) we constructed the $\pi \pi$ scattering amplitude $T_0^0$ with regular analytical properties in the $s$ complex plane, describing both experimental data and the results based on chiral expansion and Roy equations. Now the results obtained during development of our work are presented. We dwell on questions dealing with the low $\sigma -f_0$ mixing, inelasticity description and the kaon loop model for $\varphi \to \gamma (\sigma +f_0)$ reaction, and show a number of new fits. In particular, we show that the minimization of the $\sigma -f_0$ mixing results in the four-quark scenario for light scalars: the $\sigma$(600) coupling with the $K\bar{K}$ channel is suppressed relatively to the coupling with the $\pi \pi$ channel, and the $f_0$(980) coupling with the $\pi \pi$ channel is suppressed relatively to the coupling with the $K\bar{K}$ channel. The correct analytical properties of the $\pi \pi$ scattering amplitude are reached with the help of rather complicated background function. We also suggest much more simple background parameterization, practically preserving the resonance features, which is comfortable for experimental data analysis, but allows to describe the results based on chiral expansion and Roy equations only on the real $s$ axis.

24 pages, 50 figures, 7 tables

References in corpus (5)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Lightest scalar in the SU_L(2)*SU_R(2) linear σmodel
• Isospin mixing in the nucleon and 4He and the nucleon strange electric form factor
• The analytical $\pi \pi$ scattering amplitude and the light scalars

Cited by in corpus (15)

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• Light scalar mesons and two-kaon correlation functions
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• Semileptonic decays $D\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ and $D_s\to {\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ as the probe of constituent quark-antiquark pairs in the light scalar mesons
• Mechanisms of the isospin-breaking decay $f_1(1285)\to f_0(980){\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$
• Strong isospin symmetry breaking in light scalar meson production
• The $a_0(980)$ physics in semileptonic $D^0$ and $D^{+}$ decays
• Pion form factor and reactions e^+e^---> omega pi^0 and e^+e^---> pi^+ pi^- pi^+ pi^- at energies up to 2-3 GeV in the many-channel approach
• Comparative study of the production of scalar and tensor mesons in $e^{+}{e}^{-}$ collisions
• Fate of Light Scalar Mesons
• Phenomenological description of the ${\pi }^{-}{\pi }^{+}$ $S$-waves in $D^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ and $D_s^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$ decays: The problem of phases
• The reactions $\pi \pi \to \pi \pi$ and $\gamma \gamma \to \pi \pi$ in $\chi$PT with an isosinglet scalar resonance