Pion-Nucleon Scattering Amplitudes in the Range 300-700 MeV

Abstract

The cross section for the scattering of ${\pi }^{+}$ and ${\pi }^{-}$ by nucleons in the energy range 300-700 MeV has been analyzed in terms of energy-independent parameters. The parameterization is based on a dispersion relation satisfied by the partial-wave amplitudes, by replacing the left cut by a superposition of poles and the inelasticity function $R_l=\frac{{\sigma }_l\left(\mathrm{tot}\right)}{{\sigma }_l\left(\mathrm{el}\right)}$ by a ratio of polynomials in the momentum. Detailed results are presented for the real and imaginary parts of the phase shifts with $l<~3$. The structure of the "second resonance" is more complicated than has heretofore been thought, $p_{11}$, $s_{11}$, and $d_{13}$ waves all playing an important part. The width of the $d_{13}$ resonance is found to be considerably smaller than previous values from total cross-section measurements. The role of the (possibly resonant) amplitudes $p_{11}$ and $s_{11}$ is discussed.