Unitary and Crossing-Symmetric <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math>-, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-Wave Low-Energy Pion-Pion Scattering

John B. Carrotte; Robert C. Johnson

doi:10.1103/PhysRevD.2.1945

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Unitary and Crossing-Symmetric $S$ -, $P$ -, and $D$ -Wave Low-Energy Pion-Pion Scattering

John B. Carrotte^* and Robert C. Johnson

Mathematics Department, University of Durham, Durham, England

^*S. R. C. Research Student.

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Phys. Rev. D 2, 1945 – Published 1 November, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.1945

Abstract

Crossing-symmetric solutions to the pion-pion partial-wave dispersion relations are obtained, using the inverse-amplitude method. The presence of the $ρ$ meson with its physical mass and width is assumed, the amplitudes are constrained to contain Adler zeros, and general sum rules and inequalities are satisfied. Favored solutions contain a very broad isoscalar $S$ -wave resonance, and have a small decreasing isospin-2 $S$ -wave phase shift. The $D$ waves are very small. The over-all agreement with phenomenology and with other $S$ -matrix calculations is very good.

References (39)

J. W. Moffat, Phys. Rev. 121, 926 (1961)
R. H. Graham and R. C. Johnson, Phys. Rev. 188, 2362 (1969)
R. Roskies, Nuovo Cimento 66A, 494 (1970) J. L. Basdevant, G. Cohen-Tannoudji, and A. Morel, ibid. 64A, 585 (1969)
A. Martin, Nuovo Cimento 47, 265 (1967) A. K. Common, ibid. 53A, 946 (1968) G. Auberson, O. Piguet, and G. Wanders, Phys. Letters 28B, 41 (1968)
G. AubersonO. PiguetG. WandersProceedings of the Conference on $π π$ and $K π$ Interactions, edited by F. Loeffler and E. Malamud, Argonne National Laboratory Report, 1969 (unpublished)
E. P. Tryon, in [5], p. 665
D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1969) (summarized in [5], p. 726) Phys. Rev. D 1, 520 (1970)
R. C. Johnson and P. D. B. Collins, Phys. Rev. 185, 2020 (1969)
R. C. Johnson, Phys. Letters 32B, 199 (1970)
Omitted endnote
A. Yahil, Phys. Rev. 185, 1786 (1969)
S. L. Adler, Phys. Rev. 137, B1022 (1965) ibid.139, B1638 (1965)
Omitted endnote
M. G. Olsson, Phys. Rev. 162, 1338 (1967)
Omitted endnote
R. C. Johnson, Phys. Rev. D (to be published)
Particle Data Group, Rev. Mod. Phys. 41, 1 (1969)
Omitted endnote
G. F. Chew and S. Mandelstam, Phys. Rev. 119, 467 (1960)
Omitted endnote
Omitted endnote
[1]
B. H. Bransden and J. W. Moffat, Nuovo Cimento 21, 505 (1961) Phys. Rev. Letters 8, 145 (1962)
B. H. Bransden and J. W. Moffat, Nuovo Cimento 32, 159 (1964)
Omitted endnote
Omitted endnote
T. E. Kalogeropoulos, Phys. Rev. 185, 2030 (1969)
L. Dubal and M. Roos, in [5], p. 285
L. Castillejo, R. H. Dalitz, and F. J. Dyson, Phys. Rev. 101, 453 (1956)
([17])
L. S. Brown and R. L. Goble [Phys. Rev. Letters 20, 346 (1968)] [4] [2]
G. F. Chew and S. Mandelstam, Nuovo Cimento 19, 752 (1961)
Omitted endnote
L. J. Gutay, F. T. Meiere, and J. H. Scharenguivel, Phys. Rev. Letters 23, 431 (1969) D. Cline, K. J. Braun, and V. R. Scherer, Nucl. Phys. B18, 77 (1970)
J. P. Dilley, University of Ohio report, 1970 (unpublished)
F. Arbab and J. T. Donohue, Phys. Rev. D 1, 217 (1970)
Omitted endnote
[7] [6]
G. F. Chew, Phys. Rev. Letters 9, 233 (1962)

[c1] J. W. Moffat, Phys. Rev. 121, 926 (1961)

[c2] R. H. Graham and R. C. Johnson, Phys. Rev. 188, 2362 (1969)

[c3] R. Roskies, Nuovo Cimento 66A, 494 (1970) J. L. Basdevant, G. Cohen-Tannoudji, and A. Morel, ibid. 64A, 585 (1969)

[c4] A. Martin, Nuovo Cimento 47, 265 (1967) A. K. Common, ibid. 53A, 946 (1968) G. Auberson, O. Piguet, and G. Wanders, Phys. Letters 28B, 41 (1968)

[c5] G. AubersonO. PiguetG. WandersProceedings of the Conference on $π π$ and $K π$ Interactions, edited by F. Loeffler and E. Malamud, Argonne National Laboratory Report, 1969 (unpublished)

[c6] E. P. Tryon, in [5], p. 665

[c7] D. Morgan and G. Shaw, Nucl. Phys. B10, 261 (1969) (summarized in [5], p. 726) Phys. Rev. D 1, 520 (1970)

[c8] R. C. Johnson and P. D. B. Collins, Phys. Rev. 185, 2020 (1969)

[c9] R. C. Johnson, Phys. Letters 32B, 199 (1970)

[c10] Omitted endnote

[c11] A. Yahil, Phys. Rev. 185, 1786 (1969)

[c12] S. L. Adler, Phys. Rev. 137, B1022 (1965) ibid.139, B1638 (1965)

[c13] Omitted endnote

[c14] M. G. Olsson, Phys. Rev. 162, 1338 (1967)

[c15] Omitted endnote

[c16] R. C. Johnson, Phys. Rev. D (to be published)

[c17] Particle Data Group, Rev. Mod. Phys. 41, 1 (1969)

[c18] Omitted endnote

[c19] G. F. Chew and S. Mandelstam, Phys. Rev. 119, 467 (1960)

[c20] Omitted endnote

[c21] Omitted endnote

[c22] [1]

[c23] B. H. Bransden and J. W. Moffat, Nuovo Cimento 21, 505 (1961) Phys. Rev. Letters 8, 145 (1962)

[c24] B. H. Bransden and J. W. Moffat, Nuovo Cimento 32, 159 (1964)

[c25] Omitted endnote

[c26] Omitted endnote

[c27] T. E. Kalogeropoulos, Phys. Rev. 185, 2030 (1969)

[c28] L. Dubal and M. Roos, in [5], p. 285

[c29] L. Castillejo, R. H. Dalitz, and F. J. Dyson, Phys. Rev. 101, 453 (1956)

[c30] ([17])

[c31] L. S. Brown and R. L. Goble [Phys. Rev. Letters 20, 346 (1968)] [4] [2]

[c32] G. F. Chew and S. Mandelstam, Nuovo Cimento 19, 752 (1961)

[c33] Omitted endnote

[c34] L. J. Gutay, F. T. Meiere, and J. H. Scharenguivel, Phys. Rev. Letters 23, 431 (1969) D. Cline, K. J. Braun, and V. R. Scherer, Nucl. Phys. B18, 77 (1970)

[c35] J. P. Dilley, University of Ohio report, 1970 (unpublished)

[c36] F. Arbab and J. T. Donohue, Phys. Rev. D 1, 217 (1970)

[c37] Omitted endnote

[c38] [7] [6]

[c39] G. F. Chew, Phys. Rev. Letters 9, 233 (1962)

Physical Review D

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Unitary and Crossing-Symmetric $S$ -, $P$ -, and $D$ -Wave Low-Energy Pion-Pion Scattering

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Unitary and Crossing-Symmetric S-, P-, and D-Wave Low-Energy Pion-Pion Scattering

Abstract

References (39)

Unitary and Crossing-Symmetric $S$ -, $P$ -, and $D$ -Wave Low-Energy Pion-Pion Scattering