Pion-Nucleon Scattering and Structure of Fourth-Order Matrix Elements in Ps(Ps)Meson Theory

概要

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The fourth-order S-matrix elements(ME)for elastic pion-nucleon scattering at low energies are analytically evaluated by expanding in powers of mass ratio μ / M, and are analyzed in detail so as to compare relative advantages of the existing theories. The scattering phase shifts are then evaluated using the variation principle for K-matrices. It is found that the main s-wave parts of the ME contain ln(M / μ)term which has no bearing on the recoil effect and has the different sign for crossed and ladder graphs. In connection with this, the reason why the 5-box TD approximation gave essentially isotopic spin independent s-wave scattering is given. It is also suggested that the main recoil p-wave term ln(M / μ)appearing only in the crossed graphs can be a possible reason why our I=J=3 / 2, p-wave phase shift does not show resonant behavor, contrary to that in the 5-box TD methior , contrary to that in the 5-box TD method as well as the Chew and Low theory.
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