A partial-wave analysis of the reaction ${\pi }^{-}\overrightarrow{p}{\pi }^{+}{\pi }^{-}{\pi }^{-}p$ at $18\hspace{0.5em}\mathrm{GeV}/c$ has been performed on a data sample of 250 000 events obtained in the Brookhaven experiment E852. The well-known $a_1\mathrm{}\left(1260\right),$ $a_2\mathrm{}\left(1320\right)\mathrm{}$ and ${\pi }_2\mathrm{}\left(1670\right)\mathrm{}$ resonant states are observed. The existence of the $\pi \mathrm{}\left(1800\right),$ $a_1\mathrm{}\left(1700\right)\mathrm{}$ and $a_4\mathrm{}\left(2040\right)\mathrm{}$ states is confirmed. The $a_3\mathrm{}\left(1874\right)\mathrm{}$ state is also observed. The exotic $1^{-+}$ ${\pi }_1\mathrm{}\left(1600\right)\mathrm{}$ state produced in the natural parity exchange process is found to decay in the $\rho \mathrm{}\left(770\right)\mathrm{}{\pi }^{-}$ channel. A mass-dependent fit results in a resonance mass of $1593\pm 8_{-47}^{+29\mathrm{}}\hspace{0.5em}\mathrm{MeV}{/c}^2$ and a width of $168\pm {20}_{-12}^{+150\mathrm{}}\hspace{0.5em}\mathrm{MeV}{/c}^2.$

• Received 19 November 2001

DOI:https://doi.org/10.1103/PhysRevD.65.072001