$\pi\pi$ scattering and the meson resonance spectrum

W.M. Kloet; B. Loiseau

doi:doi:10.1007/s100500050067

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2023 Impact factor 2.6

Hadrons and Nuclei

Eur. Phys. J. A 1, 337-346

$\pi\pi$ scattering and the meson resonance spectrum

W.M. Kloet¹ - B. Loiseau^2,3

¹ Department of Physics and Astronomy, Rutgers University, PO Box 849, Piscataway, New Jersey 08855-0849, USA
² Division de Physique Théorique $^{\star}$ , Institut de Physique Nucléaire, F-91406, Orsay CEDEX
³ LPTPE, Université P. & M. Curie, 4 Place Jussieu, F-75252, Paris CEDEX 05, France

Received: 19 November 1997 Communicated by W. Weise

Abstract
A $\pi\pi$ , $\bar{K}K$ , and $\rho \rho$ ( $\omega \omega$ )fully coupled channel model is used to predict the lowest isospin S, P, D, F-wave phase shifts and inelasticities for elastic $\pi\pi$ scattering from threshold to 2.0 GeV. As input the S-matrix is required to exhibit poles corresponding to the meson resonance table of the Particle Data Group. As expected, the $\pi\pi$ inelasticity is very strongly related to the opening of the $\bar{K}K$ channel near 1 GeV, and the opening of $\rho \rho$ (4 $\pi$ ) and $\omega \omega$ (6 $\pi$ ) channels in the 1.5 GeV region. The predictions of this model are compared to the various elastic $\pi \pi \rightarrow \pi \pi$ amplitudes, that were obtained from analyses of $\pi^-$ p $\rightarrow$ $\pi^- \pi^+$ n data. The role of the various resonances, in particular the glueball candidate f₀(1500) and the f_J(1710) is investigated.