Prog. Theor. Phys. Vol. 38 No. 4 (1967) pp. 920-932
Pion-Nucleon Scattering at Low Energies and Partially Conserved Axial-Vector Current Hypothesis
Department of Physics, Yamagata University, Yamagata
*Department of Applied Science, Faculty of Technology, Tohoku University, Sendai
(Received March 30, 1967)
Using the axial-vector current commutation relation and the partially conserved axial-vector current hypothesis, the low energy pion-nucleon scattering amplitudes are analyzed. For the p-wave scattering amplitudes, the (3, 3)-resonance contribution which appears through the time-ordered product of the axial-vector currents is found to be the same order of magnitude as the contribution from the equal-time commutator of the axial-vector currents. By considering the (3, 3)-resonance contribution, the differences between the p-wave scattering lengths are compared with experiment. Our prediction prefers the Hamilton-Woolcock result to the Roper-Wright-Field one, but it is not very conclusive. The contribution from the equal-time commutator of the axial-vector currents is shown to be essentially that from the ρ-meson-exchange interaction. It is stressed that the PCAC meson theory is essentially the same as the derivative-coupling meson theory in consideration of contributions both from the ρ-meson-exchange interaction and probably from the π-π s-wave interaction.
DOI : 10.1143/PTP.38.920
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