A method of statistical testing of analyticity is applied to pion-pion shifts in order to obtain the pole positions in the second sheet of the complex energy plane for the resonances in the $S$, $P$, and $D$ partial waves. Whereas the positions of the dominant resonances are found at $m_{\rho }=(768\mathrm{}\pm 4)-i(74\pm 3)$ MeV, $m_{S^{*}}=(998\mathrm{}\pm 7)-i(19\pm 6)$ MeV, and $m_f=(1268\mathrm{}\pm 34)-i(94\pm 25)$ MeV, no conclusions about the $\epsilon \mathrm{}\left(1300\right)\mathrm{}$ or the ${\rho }^{\prime }\mathrm{}\left(1600\right)\mathrm{}$ could be reached.

• Received 21 March 1979

DOI:https://doi.org/10.1103/PhysRevD.21.1342