Compilation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>p</mml:mi></mml:math>Data at 4 GeV/<i>c</i>: Backward Resonance Production and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>Scattering

In ${\ensuremath{\pi}}^{\ensuremath{-}}p$ single-pion-production reactions near 4 GeV/c, we observe several interesting features. Backward ${\ensuremath{\rho}}^{0}$ production is seen to occur with $\frac{d\ensuremath{\sigma}}{\mathrm{du}}=63\ifmmode\pm\else\textpm\fi{}21$ \ensuremath{\mu}b/${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ at 180\ifmmode^\circ\else\textdegree\fi{}. Backward ${\ensuremath{\rho}}^{\ensuremath{-}}$ production is less prominent. We see evidence for production at small $u$ of ${N}^{*0}$ ($p{\ensuremath{\pi}}^{\ensuremath{-}}$ near 1700 MeV) and ${\ensuremath{\Delta}}^{\ensuremath{-}}$ ($n{\ensuremath{\pi}}^{\ensuremath{-}}$ at 1236 MeV), and possible evidence for other $n{\ensuremath{\pi}}^{\ensuremath{-}}$ structure at about 1800 MeV. The density-matrix elements for peripheral ${\ensuremath{\rho}}^{0}$ production are presented in the Jackson and in the helicity frame. The ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ elastic cross section is obtained by extrapolation of the data to the mass shell. The $S$-wave $\ensuremath{\pi}\ensuremath{\pi}$ phase shifts are calculated by two methods and compared with previous results. We find evidence in the dipion decay angular distribution for the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decay mode of the ${S}^{*}(1070)$.