Chiral symmetry amplitudes in the swave isoscalar and isovector channels and the $\sigma, f_0(980), a_0 (980)$ scalar mesons
Abstract
We use a nonpertubative approach which combines coupled channel Lippmann Schwinger equations with mesonmeson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the Swave amplitudes corresponding to the $\sigma$, f_0 and a_0 resonances. The $\pi \pi \to \pi \pi, \pi \pi \to K \bar{K}$ phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the $\pi^0 \eta$ and $K \bar{K}$ mass distributions in the T = 1 channel. Furthermore, the total and partial decay widths of the f_0 and a_0 resonances are properly reproduced including also the decay into the $\gamma \gamma$ channel. The results seem to indicate that chiral symmetry constraints at low energy and unitarity in coupled channels is the basic information contained in the mesonmeson interaction below $\sqrt{s} \simeq 1.2 GeV$.
 Publication:

arXiv eprints
 Pub Date:
 January 1996
 DOI:
 10.48550/arXiv.nuclth/9601031
 arXiv:
 arXiv:nuclth/9601031
 Bibcode:
 1996nucl.th...1031O
 Keywords:

 Nuclear Theory;
 High Energy Physics  Phenomenology
 EPrint:
 22 pages, 9 Postscript figures, LATEX. Major conceptual changes