Abstract
The dependence of the cross section for low invariant mass and small is discussed with a view toward extrapolation to the pion pole and extraction of phase shifts. There is a complicated -dependent term in the cross section which makes extrapolation inaccurate. This term can be isolated by consideration of certain moments (in the distribution with respect to the pion angles , in the dipion rest frame), if nucleon helicity flip is assumed to dominate. Indirect empirical evidence and the absorption model with exchange both support this assumption in the region. The assumption is weaker than the popular assumption that the Chew-Low pion-exchange formula holds, and can also be directly tested by examining the dependence of certain moments at 0° (forward production of the dipion). For - and -wave scattering, one considers the coefficients of 1, , and in addition to the usual -dependent terms. The coefficient of is the complicated term. It is reasonable to hope that the remaining moments are smoothly varying for , and are suitable for extrapolation. They are constrained to a definite dependence at 0° by angular momentum conservation. We feel that reliable determination of the cross section in the region and below is attainable by this method in high-statistics experiments currently under way.
- Received 3 September 1968
DOI:https://doi.org/10.1103/PhysRev.177.2353
©1969 American Physical Society