Unitarization, Castillejo-Dalitz-Dyson Poles, and Scalar Companions

Ronald Rockmore
Phys. Rev. D 4, 900 – Published 1 August 1971

Abstract

It is shown how Castillejo-Dalitz-Dyson poles may be introduced into the effective-range formulas for scalar (I=J=0) ππ and (I=J=12) Kπ 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 s-wave amplitude. In the case of the s-wave ππ phase-shift fit, the remaining three parameters are fixed by requiring the 0+ resonances, ε(750) and ε(1060), and the experimentally observed value (in the up-up data) of δ00(ππ)π at 900 MeV as input. The resulting fit is nearly indistinguishable from the earlier two-parameter fit which uses only the ε, 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 [ε(698) and ε(911)] differ somewhat. Considerably greater variation in fit is found in the case of the s-wave Kπ phase shift; a qualitative fit to the up-up data of Antich et al. is obtained using κ(900), κ(1600), and δ0(12)(Kπ)π at 1000 MeV.

  • Received 16 April 1971

DOI:https://doi.org/10.1103/PhysRevD.4.900

©1971 American Physical Society

Authors & Affiliations

Ronald Rockmore

  • Department of Physics, Rutgers—The State University, New Brunswick, New Jersey 08903

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Issue

Vol. 4, Iss. 3 — 1 August 1971

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