  Model independent amplitude analyses of $\pi^- p_\uparrow \to \pi^- \pi^+ n$
on polarized target at 17.2 GeV/c reveal resonant structure of S-wave
transversity amplitudes $|\bar S|^2\Sigma$ and $|S|^2\Sigma$ near 750 MeV.
Simultaneous fit to $|\bar S|^2\Sigma$ and $|S|^2\Sigma$ with a single $\sigma$
pole yields $m_\sigma = 775 \pm 17$ MeV and $\Gamma_\sigma = 147 \pm 33$ MeV.
Simultaneous fit with two common $\sigma$ poles yields a lower $\chi^2/dpt$.
Their resonance parameters are $m_\sigma = 786 \pm 24$ MeV, $\Gamma_\sigma =
130 \pm 47$ MeV and $m_{\sigma^\prime} = 670 \pm 30$ MeV,
$\Gamma_{\sigma^\prime} = 59 \pm 58$ MeV.
