Study of resonant structure of S-wave amplitudes in pi(-)p->pi(-)pi(+)n measured on polarized target at 17.2 GeV/c in the mass range of 580-1080 MeV

We have performed a new model independent amplitude analysis of reaction ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ measured at CERN at 17.2 GeV/c on polarized target. The analysis extends the range of dipion mass from 600–880 MeV used in the previous study to 580–1080 MeV. Our purpose is to study the role of $f_0(980)$ interference and to better determine the resonance parameters of $\sigma (750)$ resonance from fits to both S-wave amplitudes $\mathrm{\mid }\bar{S}{\mathrm{\mid }}^2\mathrm{\Sigma }$ and $\mathrm{\mid }S{\mathrm{\mid }}^2\mathrm{\Sigma }$ with recoil nucleon transversities up'' and down’', respectively. This work is the first attempt to determine resonance parameters of a resonance from Breit-Wigner fits to production amplitudes of opposite transversity. We used several fitting procedures to understand the resonant structure of the S-wave amplitudes in this mass range. The simultaneous fit to $\mathrm{\mid }\bar{S}{\mathrm{\mid }}^2\mathrm{\Sigma }$ and $\mathrm{\mid }S{\mathrm{\mid }}^2\mathrm{\Sigma }$ with two common $\sigma$ poles yields an excellent fit with a lower ${\chi }^2\mathrm{/}dpt$ than the separate fits. All amplitudes are dominated by a $\sigma$ state with $m_{\sigma }=786\pm 24$ MeV and ${\mathrm{\Gamma }}_{\sigma }=130\pm 47$ MeV. All amplitudes receive a weaker contribution from a narrower ${\sigma }^{\mathrm{\prime }}$ state with $m_{{\sigma }^{\mathrm{\prime }}}=670\pm 30$ MeV and ${\mathrm{\Gamma }}_{{\sigma }^{\mathrm{\prime }}}=59\pm 58$ MeV. We propose to identify ${\sigma }^{\mathrm{\prime }}(670)$ and $\sigma (786)$ with colour-electric and colour-magnetic modes of lowest mass scalar gluonium $0^{++}(gg)$.