MODIFIED EXTRAPOLATION TO DETERMINE PI PI CROSS SECTION

The dependence of the π+N→(2π)+N cross section for low invariant ππ mass and small t is discussed with a view toward extrapolation to the pion pole and extraction of ππ phase shifts. There is a complicated t-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 θ in the dipion rest frame), if nucleon helicity flip is assumed to dominate. Indirect empirical evidence and the absorption model with π exchange both support this assumption in the 5-10-BeVc 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 t dependence of certain moments at 0°(forward production of the dipion). For s- and p-wave ππ scattering, one considers the coefficients of 1, cosθ, and sin2θ in addition to the usual dependent terms. The coefficient of sin2θ 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 t dependence at by angular momentum conservation. We feel that reliable determination of the ππ cross section in the ρ region and below is attainable by this method in high-statistics experiments currently under way. © 1969 The American Physical Society.