S-wave pi pi scattering and the S poles

The I=0 S-wave pi pi scattering amplitude is analysed with a primary interest in the S/sup */. The amplitude corresponding to the S/sup */ is parametrized in terms of pole positions. The recent CERN-Munich energy-independent partial-wave solution is reproduced better by an amplitude with two poles (on sheet II and sheet III) than by that with only one pole (on sheet II). The background phase is also analysed in detail and the long conjectured existence of the epsilon (700) is almost excluded. (20 refs).