Pion-Pion Scattering Below 850 MeV. A Unique Solution

David Morgan; Graham Shaw

doi:10.1103/PhysRevD.2.520

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Pion-Pion Scattering Below 850 MeV. A Unique Solution

David Morgan

Graham Shaw

Rutherford Laboratory, Berkshire, England

Columbia University, New York, New York 10027

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Phys. Rev. D 2, 520 – Published 1 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.520

Abstract

Forward dispersion relations are used as the basis of an analysis of the information on pion-pion scattering available up to 850 MeV. These are shown to result in a model-independent relation between the scattering lengths $α_{0}$ and $α_{2}$ , valid for all possible behaviors of ${δ_{0}}^{0}$ in the $ρ$ -region, and taking the value $\frac{a_{0}}{a_{2}} = - 3.2 \pm 1.0$ from recent low-energy work, the values $a_{0} = 0.16 \pm 0.04$ , $a_{2} = - 0.05 \pm 0.01$ uniquely result. The ambiguity in ${δ_{0}}^{0}$ in the $ρ$ region is also studied, by four different methods, and uniquely resolved, allowing a detailed picture of all the phases up to 850 MeV to be given.

References (31)

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A. Donnachie, in Particle Interactions at High Energies (Oliver and Boyd, London, 1967)
D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1968)
J. H. Scharenguivel et al., Phys. Rev. 186, 1397 (1969)
L. J. Gutay, F. T. Meiere, and J. H. Scharenguivel, Phys. Rev. Letters 23, 431 (1969)
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D. Cline, K. J. Braun, and V. R. Scherer, in Proceedings of the Conference on $π π$ and $π K$ Interactions, Argonne National Laboratory, 1969 (unpublished)
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([4]); Sec. IV C
E. Malamud and P. E. Schlein, Phys. Rev. Letters 19, 1056 (1967)
Omitted endnote
S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968)
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Omitted endnote
Omitted endnote
G. Veneziano, Nuovo Cimento 57A, 190 (1968)
[4]
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[c1] S. Weinberg, Phys. Rev. Letters 17, 616 (1966)

[c2] J. Yellin and J. Shapiro (unpublished) J. Shapiro, Phys. Rev. 179, 1345 (1969) C. Lovelace, Phys. Letters 28B, 264 (1968)

[c3] A. Donnachie, in Particle Interactions at High Energies (Oliver and Boyd, London, 1967)

[c4] D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1968)

[c5] J. H. Scharenguivel et al., Phys. Rev. 186, 1397 (1969)

[c6] L. J. Gutay, F. T. Meiere, and J. H. Scharenguivel, Phys. Rev. Letters 23, 431 (1969)

[c7] D. Cline, K. J. Braun, and F. R. Scherer, University of Wisconsin Report, 1969 (unpublished)

[c8] W. Deinet et al., Phys. Letters 30B, 359 (1969)

[c9] D. Cline, K. J. Braun, and V. R. Scherer, in Proceedings of the Conference on $π π$ and $π K$ Interactions, Argonne National Laboratory, 1969 (unpublished)

[c10] R. Bizzarri et al., Nucl. Phys. B14, 169 (1969)

[c11] Proceedings of the Conference on $π π$ and $π K$ Interactions, Argonne National Laboratories, 1969 (unpublished)

[c12] S. U. Chung et al., Phys. Rev. 165, 1491 (1968)

[c13] ([4]); Sec. IV C

[c14] E. Malamud and P. E. Schlein, Phys. Rev. Letters 19, 1056 (1967)

[c15] Omitted endnote

[c16] S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968)

[c17] E. Malamud and P. E. Schlein in [11]

[c18] W. D. Walker, J. Carroll, A. Garfinkel, and B. Oh, Phys. Rev. Letters 18, 630 (1967)

[c19] J. P. Baton, G. Laurens, and J. Reignier, Nucl. Phys. B3, 349 (1967)

[c20] Omitted endnote

[c21] Omitted endnote

[c22] G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c23] [4]

[c24] W. Rarita, R. J. Riddell, C. B. Chiu, and R. J. N. Phillips, Phys. Rev. 165, 1615 (1968)

[c25] R. Roskies, Phys. Letters 30B, 42 (1969) Nuovo Cimento 65A, 467 (1970)

[c26] G. Auberson, O. Piguet, and G. Wanders, Phys. Letters 28B, 41 (1968)

[c27] ([17]) [19] C. D. Froggatt and D. Morgan, Phys. Rev. 187, 2044 (1969) ([19])

[c28] C. Lovelace, [11]

[c29] M. G. Olsson, Phys. Rev. 162, 1338 (1967)

[c30] N. N. Biswas et al., Phys. Rev. D 1, 2705 (1970)

[c31] N. N. Biswas, [11]

Physical Review D

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Pion-Pion Scattering Below 850 MeV. A Unique Solution

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References (31)

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