Scalar mesons and low-mass sigma: Does the $\sigma$ reveal the confinement singularity?

Abstract

I present a short review of the current understanding of the scalar meson sector, with special attention to the problem of the low-mass $\sigma$. The dispersion relation $N/D$-method used for the restoration of the low-energy $\pi \pi$ $(I{J}^{PC}=00^{++})$-wave amplitude is discussed. The low-energy $\pi \pi$ amplitude was determined from the data in the energy region 280--500 MeV and it was sewn with the previously found $K$-matrix solution for the region 450--1950 MeV. The $N/D$-amplitude has a pole on the second sheet of the complex-$s$ plane, near the $\pi \pi$ threshold at $\sqrt{s}\simeq 430-i325$ MeV, that corresponds to the low-mass $\sigma$-meson. I discuss the hypothesis that this pole may be related to the confinement forces, thus being the eyewitness of confinement.

27 pages, 13 figure

References in corpus (4)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• Four Sorts of Mesons
• K-matrix analysis of the (IJ^{PC}=00^{++})-wave in the mass region below 1900 MeV
• Radiative Scalar Meson Decays in the Light-Front Quark Model

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• Multichannel Anomaly of the Resonance Pole Parameters Resolved
• On nature of the scalar-isoscalar mesons in the uniformizing-variable method based on analyticity and unitarity
• Properties of the ${\pi }^0$, $\eta$, ${\eta }^{\prime }$, $\sigma$, $f_0(980)$ and $a_0(980)$ mesons and their relevance for the polarizabilities of the nucleon
• 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
• Poles, the only true resonant-state signals, are extracted from a worldwide collection of partial wave amplitudes using only one, well controlled pole-extraction method
• Baryon-baryon and baryon-antibaryon interaction amplitudes in the spin--momentum operator expansion method