A chiral-perturbative consideration of the near-threshold reaction indicates that the pion-rescattering term has a substantial energy and momentum dependence. The existing calculations that incorporate this dependence give pion rescattering contributions significantly larger than those of the conventional treatment, and this enhanced rescattering term interferes destructively with the one-body impulse term, leading to theoretical cross sections that are much smaller than the observed values. However, since the existing calculations are based on coordinate-space representation, they involve a number of simplifying assumptions about the energy-momentum flow in the rescattering diagram, even though the delicate interplay between the one-body and two-body terms makes it desirable to avoid these kinematical assumptions. We carry out here a momentum-space calculation that retains the energy-momentum dependence of the vertices as predicted by chiral perturbation theory. Our improved treatment increases the rescattering amplitude by a factor of 3 over the value obtained in the -space calculations. The transition amplitude, which is now dominated by the rescattering term, leads to the cross section much larger than what was reported in the approximate -space calculations. Thus, the extremely small cross sections obtained in the previous chiral perturbative treatments of this reaction should be considered as an accidental consequence of the approximations employed rather than a general feature.
- Received 3 April 1997
- Published in the issue dated September 1997
© 1997 The American Physical Society