Abstract
A relativistic model for pion-nucleon elastic scattering is derived by assuming pseudoscalar coupling and suppressing the contribution of the intermediate antinucleon states. This model is suggested as a relativistic extension of the Chew-Low model, which contains no antinucleons. Furthermore, the antinucleons in the pseudoscalar coupling were considered to give only a small contribution in the P-waves, while being responsible for a large S-wave phase shift not observed experimentally. Starting with the transition matrix for the lowest order Feynman graphs of the pseudoscalar coupling, the propagator for the intermediate nucleons is decomposed and the antinculeons separated. The transition matrix is then decomposed into its isospin and angular momentum channels. These Born term partial wave helicity amplitudes are used as driving terms of a partial wave N over D method. Crossing is included in the infinute mass limit only. The results for crossing and the noncrossing approximation are examined. It was found that the antinucleons contribute significantly in the P-waves. In the S-waves their absence led to phase shifts much smaller than those observed experimentally. With or without the antinucleons, the S11 channel was too repulsive. The P33 crossing symmetric case gives a poor fit without the antinucleons. The pseudovector coupling was qualitatively examined as an alternative, but has the wrong sign in the P11 channel. In the noncrossing case, the pseudoscalar coupling with and without intermediate antinucleons give a good fit to the P13, P31 and P33 channels by varying the coupling f^2. The P11 channel stays repulsive thus cannot fit the experimental phase shifts. In the S-waves a fit to the phase shifts could not be obtained by varying both the vertex function and the coupling. It is shown that the intermediate antinucleons are important to the P-wave scattering. The validity of the Chew-Low model is shown to be poorly founded on physical grounds. The pseudoscalar coupling does well in the P33 and P13 channels, but not well in the j equal to one-half channels. This shows that the scalar part of the pseudoscalar coupling is inconsistant with nature, and that a [sigma] model may be more correct.
McLeod, Robert John (1979). Field theoretic model of low energy pion-nucleon elastic scattering. Doctoral dissertation, Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -145513.