Further study of the $\pi\pi$ S-wave isoscalar amplitude below the $K\overline{K}$ threshold

We continue the analysis of S-wave production amplitudes for the reaction pi /sup -/p to pi /sup +/ pi /sup -/n involving the data obtained by the CERN-Cracow-Munich collaboration on a transversely polarized target at 17.2 GeV/c pi /sup $/momentum. This study deals with the region below the KK threshold. In particular, we study the "up-steep" solution containing a narrow S-wave resonance under the rho (770). This solution exhibits a considerable inelasticity eta which does not have any physical interpretation. Assuming that this inelasticity behaviour represents an unlikely fluctuation we impose eta identical to 1 for all data points. This leads to non-physical results in one third of the pi /sup +/ pi /sup -/ effective mass bins and in the remaining mass bins some parameters behave in a queer way. The situation is even worse for the "down-steep" solution. We conclude that the 17.2 GeV data cannot be described by a relatively narrow f/sub 0/(750). The "down-flat" and "up-flat" solutions which easily pass the eta identical to 1 constraint exhibit a slow increase of phase shifts in the rho (770) mass range. (24 refs).