ππ Phase Shift Analysis

We perform an energy independent ππ phase shift analysis in the energy range $\text{440\hspace{0.17em}<\hspace{0.17em}}{\mathrm{M}}_{\mathrm{\pi \pi }}\text{\hspace{0.17em}<\hspace{0.17em}<\hspace{0.17em}1400\hspace{0.17em}}\mathrm{MeV}$ using high statistics ${\pi }^{-}\mathrm{p}{\mathrm{\Rightarrow \pi }}^{-}{\pi }^{+}\mathrm{n}$ data at 17.2 GeV/c. The method is based on an amplitude analysis of the production process and the extrapolation of the dominant π exchange amplitudes to the π exchange pole. We consider the phase shift ambiguities and study ways of selecting the physical solution. We determine the parameters of the ρ and f resonances. We find an $\mathrm{I}\text{\hspace{0.17em}=\hspace{0.17em}0}$ S wave resonance under the f and we comment on the properties of the S^* resonance near the KK threshold.