Single-Pion Production inπ−pInteractions at 2.26 GeV/c

We present an analysis of $\pi \pi N$ final states obtained from ${\pi }^{-}p$ interactions at 2.26 GeV/c. Strong $\rho$ production is present in both final states. In addition, significant nucleon isobar production is observed. We observed the following cross sections: $\sigma \left({\pi }^{-}{\pi }^{0}p\right)=3.77\mathrm{}\pm 0.13$ mb, $\sigma \left({\pi }^{-}{\pi }^{+}n\right)=5.67\mathrm{}\pm 0.17$ mb, $\sigma \left({\rho }^{-}p\right)=2.19\mathrm{}\pm 0.09$ mb, $\sigma \left({\Delta }^{+}\mathrm{}\right(1236\left)\mathrm{}{\pi }^{-}\right)=0.30\mathrm{}\pm 0.10$ mb, $\sigma \left(N^0\mathrm{}\right(1650\left)\mathrm{}{\pi }^0\right)=0.49\mathrm{}\pm 0.07$ mb, $\sigma \left({\rho }^{0}n\right)=2.89\mathrm{}\pm 0.11$ mb, $\sigma \left({\Delta }^{-}\mathrm{}\right(1236\left)\mathrm{}{\pi }^{+}\right)=0.11\mathrm{}\pm 0.06$ mb, $\sigma \left(N^{+}\mathrm{}\right(1470\left)\mathrm{}{\pi }^{-}\right)=0.24\mathrm{}\pm 0.06$ mb, and $\sigma \left(N^{+}\mathrm{}\right(1650\left)\mathrm{}{\pi }^{-}\right)=0.45\mathrm{}\pm 0.05$ mb. The spin-density matrix elements are determined for the ${\rho }^0$ by interpreting the ${\rho }^0$ asymmetry as an interference between the resonant $P$ wave and a $T=0\mathrm{}$ $S$ wave. A search for the ${\epsilon }^0$ in the ${\pi }^{+}{\pi }^{-}n$ final state failed to yield a direct observation of this effect.