Pion-deuteron dispersion relations in impulse approximation

Abstract

Dispersion relations for pion-deuteron forward scattering π+D → π+D are discussed by using the impulse approximation for the calculation of the contribution in the unphysical region which is due to the absorptive process π+D→N+N. Special regard is taken to the anomalous situation which is investigated by explicit analytic continuation of the contribution from the absorptive process in the dispersion relations with respect to the pion mass. It is found that an anomalous logarithmic branch point and an anomalous pole appear at the same point, which coincides with that found in perturbation theory where the deuteron is treated as elementary. It turns out that the anomalous situation is only governed by the asymptotic behaviour of the occuring deuteron wave functions. It is further shown that the spin-flip dispersion relation can be used for a determination of the pion-nucleon coupling constant. The value found by employing the impulse approximation for the spin-flip amplitude in the observable region of the dispersion relation agrees within 10% with that following from the corresponding pion-nucleon dispersion relation. For this agreement the consideration of the anomalous pole contribution is necessary.