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

Abstract

A new analysis of S-wave production amplitudes for the reaction ${\pi }^{-}{p}_{\uparrow }\to {\pi }^{+}{\pi }^{-}n$ 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 $f_0(1500)$.

Comments: 25 Latex pages + 15 Postscript figures