Remarks on the fixed extended source pion theory

Cini and Fubini’s analysis on the possibility whether the fixed extended source pion theory can reproduce the low energy experimentalp-wave pion-nucleon scattering cross-sections is reinvestigated in the light of the restrictions: (i) The requirement that the probability can not be negative imposes some restrictions on the expectation values of the operatorsτα,σl andτασlσl, and (ii) there is a geometrical limitation on the scattering cross-section. It becomes clear that, as far as the contribution to Cini and Fubini’s sum rules from the high energy region (above cut-off) is small, the theory can not reproduce the experimental scattering cross-sections, even for the low energy region (pion kinetic energy ≲ 300 MeV). However, there is no reason to consider that the high energy contribution be small. On the other hand, it is almost certain that the theory can reproduce the experimentalp-wave pion nucleon scattering cross-section for the low energy region. This implies that the high energy contribution to Cini and Fubini’s sum rules is important and should not be neglected.