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

Ronald Rockmore

doi:10.1103/PhysRevD.4.900

Access by Xinjiang University

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

Ronald Rockmore

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

PDF

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

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

Abstract

It is shown how Castillejo-Dalitz-Dyson poles may be introduced into the effective-range formulas for scalar $(I = J = 0) π π$ and $(I = J = \frac{1}{2}) K π$ 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 $π π$ 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 $δ_{00} (π π) ≃ π$ 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 $K π$ phase shift; a qualitative fit to the up-up data of Antich et al. is obtained using $κ (900)$ , $κ^{'} (1600)$ , and ${δ_{0}}^{(\frac{1}{2})} (K π) ≃ π$ at 1000 MeV.

References (15)

J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 23, 666 (1969)
R. Rockmore, Phys. Rev. Letters 24, 541 (1970) ibid.24, 970(E) (1970)
J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 25, 67 (1970)
R. Rockmore, Phys. Rev. D 2, 2628 (1970)
R. Rockmore, Phys. Rev. D 2, 2693 (1970)
[1,3] [4,5]
[4]
J. H. Scharenguivel et al., Phys. Rev. 186, 1387 (1969)
P. Antich et al., in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 508
L. J. Gutay, in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, [9], p. 241 B. Maglić, Rapporteur's talk, in Proceedings of the Lund International Conference on Elementary Particles, 1969, edited by G. von Dardel (Berlingska, Lund, Sweden, 1970)
S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968)
W. Deinet et al., Phys. Letters 30B, 359 (1969)
[2]
Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)
C. Lovelace, in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, [9], p. 562

[c1] J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 23, 666 (1969)

[c2] R. Rockmore, Phys. Rev. Letters 24, 541 (1970) ibid.24, 970(E) (1970)

[c3] J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 25, 67 (1970)

[c4] R. Rockmore, Phys. Rev. D 2, 2628 (1970)

[c5] R. Rockmore, Phys. Rev. D 2, 2693 (1970)

[c6] [1,3] [4,5]

[c7] [4]

[c8] J. H. Scharenguivel et al., Phys. Rev. 186, 1387 (1969)

[c9] P. Antich et al., in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969), p. 508

[c10] L. J. Gutay, in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, [9], p. 241 B. Maglić, Rapporteur's talk, in Proceedings of the Lund International Conference on Elementary Particles, 1969, edited by G. von Dardel (Berlingska, Lund, Sweden, 1970)

[c11] S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968)

[c12] W. Deinet et al., Phys. Letters 30B, 359 (1969)

[c13] [2]

[c14] Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)

[c15] C. Lovelace, in Proceedings of a Conference on $π π$ and $K π$ Interactions at Argonne National Laboratory, 1969, [9], p. 562

Physical Review D

Export citation

Export citation

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

Abstract

References (15)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation