Spin-rotation parameters $A$ and $R$ for ${\pi }^{+}p$ and ${\pi }^{-}p$ elastic scattering from 427 to 657 MeV/c

The spin-rotation parameters $A$ and $R$ and the related spin-rotation angle $\beta$ have been measured for ${\pi }^{+}p$ and ${\pi }^{-}p$ elastic scattering using protons polarized in the scattering plane. The pion-beam momenta are 427, 471, 547, 625, and 657 MeV/c and the angular range is $-0.9\mathrm{}\le {cos\Theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\le 0.3$. The scattered pion and recoil proton were detected in coincidence, using a scintillator hodoscope for the pions, and the Large Acceptance Spectrometer combined with the JANUS polarimeter for the recoil protons. The results are compared with the four recent $\pi N$ partial wave analyses (PWA's). Our data show that the major features of these PWA's are correct. The $A$ and $R$ measurements complete our program of pion-nucleon experiments, providing full data sets at three of the above beam momenta. Such sets can be used to test the constraints in the PWA's or to obtain a model-independent set of $\pi N$ scattering amplitudes.