Separation of S- wave pseudoscalar and pseudovector amplitudes in pi^- p---> pi^+ pi^- n reaction on polarized target

A new analysis of S-wave production amplitudes for the reaction $\pi^- p_{\uparrow} \rightarrow \pi^+ \pi^- n$ on a transversely polarized target is performed. It is based on the results obtained by the CERN-Cracow -Munich collaboration in the pion-pion energy range from 600 MeV to 1600 MeV at 17.2 GeV/c $\pi^-$ momentum. Energy-independent separation of the S-wave pseudoscalar amplitude ($\pi$ exchange) from the pseudovector amplitude ($a_{1}$ exchange) is carried out using assumptions much weaker than those in all previous analyses. We show that, especially around 1000 MeV and around 1500 MeV, the $a_{1}$ exchange amplitude cannot be neglected. The scalar-isoscalar $\pi\pi$ phase shifts are calculated using fairly weak assumptions. Below the $K\overline{K}$ threshold we find two solutions for the $\pi-\pi$ phase shifts, for which the phases increase slower with the effective $\pi-\pi$ mass than the P-wave phases. Both solutions are consistent with a broad $f_{0}(500)$ but only one is similar to the well-known "down" solution. We find also the third solution (with a somewhat puzzling behavior of inelasticity) which exhibits a narrow $f_{0}(750)$ claimed by Svec. All the solutions undergo a rapid change at the $K\overline{K}$ threshold. Above 1420 MeV the phase shifts increase with energy faster than those obtained without the polarized-target data. This phase behavior as well as an increase of the modulus of the $a_{1}$-exchange amplitude can be due to the presence of the $f_{0}(1500)$.