Abstract
It is shown how Castillejo-Dalitz-Dyson poles may be introduced into the effective-range formulas for scalar and form factors derived from current algebra and a method of pole and cut dominance. The restriction to only two such poles leads to formulas characterized by four free parameters, one of which is conventionally fitted to the zero of the soft-meson -wave amplitude. In the case of the -wave phase-shift fit, the remaining three parameters are fixed by requiring the resonances, and , and the experimentally observed value (in the up-up data) of at 900 MeV as input. The resulting fit is nearly indistinguishable from the earlier two-parameter fit which uses only the , over the energy range from threshold to 800 MeV, and is very close to that of the unitarized Lovelace-Veneziano model from threshold to 1060 MeV, although the resonance parameters in the latter fit [ and ] differ somewhat. Considerably greater variation in fit is found in the case of the -wave phase shift; a qualitative fit to the up-up data of Antich et al. is obtained using , , and at 1000 MeV.
- Received 16 April 1971
DOI:https://doi.org/10.1103/PhysRevD.4.900
©1971 American Physical Society