Factorization of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>J</mi></mrow></msup></mrow><mi>π</mi><mo>→</mo><mrow><msup><mrow><mi>M</mi></mrow><mrow><mrow><msup><mrow><mi>J</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></mrow></msup></mrow><mi>π</mi></math></span> Residues within the Veneziano Model

Matthew A. Jacobs

doi:10.1103/PhysRevD.2.2431

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Factorization of $M^{J} π \to M^{J^{'}} π$ Residues within the Veneziano Model

Matthew A. Jacobs

Department of Physics and Astronomy, Tel-Aviv University, Ramat-Aviv, Israel

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Phys. Rev. D 2, 2431 – Published 15 November, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.2431

Abstract

The reactions $M^{J} π \to M^{J^{'}} π$ are analyzed for a class of mesons, $M^{J}$ . Imposing the Veneziano form in one channel, the Regge residues at poles are required to satisfy factorization conditions. These conditions are expressed in terms of the residues of the invariant amplitudes of the processes, for various hypotheses about the spacing of contributing trajectories of opposite normality. We find that factorization in one channel only is consistent with the coupling of the lowest-spin kinematically allowed particles in each helicity amplitude.

References (20)

G. Veneziano, Nuovo Cimento 57A, 190 (1968)
G. Canning, Nucl. Phys. B17, 359 (1970) E. S. Abers and V. L. Teplitz, Phys. Rev. Letters 22, 909 (1969) A. Capella, C. A. Savoy, and A. Villani, Nuovo Cimento Letters 2, 137 (1969) A. Capello, B. Diu, J. M. Kaplan, and D. Schiff, Nuovo Cimento 64A, 361 (1969) E. S. Abers and V. L. Teplitz, Phys. Rev. D 1, 624 (1970) M. A. Jacobs, presented at Boulder Conference on High Energy Physics, Boulder, Colorado, 1969 (unpublished) P. Carruthers and F. Cooper, Phys. Rev. D 1, 1223 (1970) M. L. Whippman ibid. 1, 701 (1970) P. Carruthers and E. Lasley, ibid. 1, 1204 (1970)
Shan-Yuan Chu and Bipin Desai, Phys. Rev. 188, 2215 (1969) S. Fenster and K. C. Wali, Phys. Rev. D 1, 1409 (1970) J. Namyslowski and M. Sawicki (unpublished) R. H. Graham and J. W. Moffat (unpublished) M. L. Blackmon and K. C. Wali (unpublished) R. F. Amann, Phys. Rev. D 2, 561 (1970) J. Maharana and R. Ramachandran (unpublished) M. H. Vaughn and D. Y. Wong (private communication)
M. A. Jacobs, Phys. Rev. 184, 1574 (1969) R. H. Mutter (unpublished) B. K. Pal (unpublished)
C. Lovelace, Review paper at the Irvine Conference on Regge Poles, 1969 (unpublished)
C. J. Goebel, M. L. Blackmon, and K. C. Wali, Phys. Rev. 182, 1485 (1969)
G. P. Canning, Nucl. Phys. B14, 437 (1969)
D. Y. Wong, Phys. Rev. 183, 1412 (1969) H. Harari, Phys. Rev. Letters 20, 1395 (1968) J. L. Rosner, ibid. 21, 950 (1968) C. B. Chiu and J. Finkelstein, Phys. Letters 27B, 510 (1968)
G. P. Canning, Nucl. Phys. B17, 359 (1970)
A. C. Hearn, Nuovo Cimento 21, 333 (1961)
M. A. Jacobs ([2]) R. E. Kreps and M. S. Milgran, Phys. Rev. D 1, 2271 (1970) M. J. Whippman, ibid.1 701 (1970)
C. Lovelace ([5]) J. Mandula, J. Weyers, and G. Zweig, Phys. Rev. Letters 23, 266 (1969) G. P. Canning, this issue, Phys. Rev. D 2, 2426 (1970)
D. Y. Wong, Phys. Rev. 181, 1900 (1969) M. A. Jacobs ([2])
D. Y. Wong ([8])
M. Jacob and G. C. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)
M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, Phys. Rev. 133, B145 (1964)
M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960) A. O. Barut, Theory of the Scattering Matrix (Macmillan, New York, 1967)
Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
C. Lovelace, Phys. Letters 28B, 265 (1968) D. Y. Wong ([8]) K. V. Vasavada, Phys. Rev. D 1, 88 (1970)
Omitted endnote

[c1] G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c2] G. Canning, Nucl. Phys. B17, 359 (1970) E. S. Abers and V. L. Teplitz, Phys. Rev. Letters 22, 909 (1969) A. Capella, C. A. Savoy, and A. Villani, Nuovo Cimento Letters 2, 137 (1969) A. Capello, B. Diu, J. M. Kaplan, and D. Schiff, Nuovo Cimento 64A, 361 (1969) E. S. Abers and V. L. Teplitz, Phys. Rev. D 1, 624 (1970) M. A. Jacobs, presented at Boulder Conference on High Energy Physics, Boulder, Colorado, 1969 (unpublished) P. Carruthers and F. Cooper, Phys. Rev. D 1, 1223 (1970) M. L. Whippman ibid. 1, 701 (1970) P. Carruthers and E. Lasley, ibid. 1, 1204 (1970)

[c3] Shan-Yuan Chu and Bipin Desai, Phys. Rev. 188, 2215 (1969) S. Fenster and K. C. Wali, Phys. Rev. D 1, 1409 (1970) J. Namyslowski and M. Sawicki (unpublished) R. H. Graham and J. W. Moffat (unpublished) M. L. Blackmon and K. C. Wali (unpublished) R. F. Amann, Phys. Rev. D 2, 561 (1970) J. Maharana and R. Ramachandran (unpublished) M. H. Vaughn and D. Y. Wong (private communication)

[c4] M. A. Jacobs, Phys. Rev. 184, 1574 (1969) R. H. Mutter (unpublished) B. K. Pal (unpublished)

[c5] C. Lovelace, Review paper at the Irvine Conference on Regge Poles, 1969 (unpublished)

[c6] C. J. Goebel, M. L. Blackmon, and K. C. Wali, Phys. Rev. 182, 1485 (1969)

[c7] G. P. Canning, Nucl. Phys. B14, 437 (1969)

[c8] D. Y. Wong, Phys. Rev. 183, 1412 (1969) H. Harari, Phys. Rev. Letters 20, 1395 (1968) J. L. Rosner, ibid. 21, 950 (1968) C. B. Chiu and J. Finkelstein, Phys. Letters 27B, 510 (1968)

[c9] G. P. Canning, Nucl. Phys. B17, 359 (1970)

[c10] A. C. Hearn, Nuovo Cimento 21, 333 (1961)

[c11] M. A. Jacobs ([2]) R. E. Kreps and M. S. Milgran, Phys. Rev. D 1, 2271 (1970) M. J. Whippman, ibid.1 701 (1970)

[c12] C. Lovelace ([5]) J. Mandula, J. Weyers, and G. Zweig, Phys. Rev. Letters 23, 266 (1969) G. P. Canning, this issue, Phys. Rev. D 2, 2426 (1970)

[c13] D. Y. Wong, Phys. Rev. 181, 1900 (1969) M. A. Jacobs ([2])

[c14] D. Y. Wong ([8])

[c15] M. Jacob and G. C. Wick, Ann. Phys. (N. Y.) 7, 404 (1959)

[c16] M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, Phys. Rev. 133, B145 (1964)

[c17] M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960) A. O. Barut, Theory of the Scattering Matrix (Macmillan, New York, 1967)

[c18] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c19] C. Lovelace, Phys. Letters 28B, 265 (1968) D. Y. Wong ([8]) K. V. Vasavada, Phys. Rev. D 1, 88 (1970)

[c20] Omitted endnote

Physical Review D

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Factorization of $M^{J} π \to M^{J^{'}} π$ Residues within the Veneziano Model

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Factorization of MJπ→MJ′π Residues within the Veneziano Model

Abstract

References (20)

Factorization of $M^{J} π \to M^{J^{'}} π$ Residues within the Veneziano Model