Partial-Wave Production Amplitudes and the Diagonalization of the Unitarity Relations in the Helicity Formalism

Kuo-Hsiang Wang

doi:10.1103/PhysRevD.4.489

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Partial-Wave Production Amplitudes and the Diagonalization of the Unitarity Relations in the Helicity Formalism

Kuo-Hsiang Wang

Physics Department, The Pennsylvania State University, University Park, Pennsylvania 16802

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Phys. Rev. D 4, 489 – Published 15 July, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.489

Abstract

A general study is made of the partial-wave amplitudes and their unitarity relations for the general $N$ -body-to- $N$ -body process in the helicity formalism. The partial-wave amplitude is so defined that it is a function of the subenergies that correspond to the noncoincident poles in a tree diagram. The partial-wave unitarity relations introduced here are diagonalized, and may supply the basis for introducing new models or improving others. The Wigner rotations and the crossing angles in the partial-wave expansion are explicitly given in terms of invariant variables. Some related topics such as the partial-wave recoupling condition, recoupling coefficients, etc., are discussed. The expressions obtained here can be applied to multiperipheral models and others. As a simple example, the contributions, elastic and inelastic, to the partial-wave amplitude via unitarity are obtained in a model of direct-channel scalar-meson dominance, with some approximations.

References (39)

G. F. Chew, M. L. Goldberger, and F. E. Low, Phys. Rev. Letters 22, 208 (1969)
I. G. Halliday, Nuovo Cimento 60A, 177 (1969) I. G. Halliday and L. M. Saunders, ibid. 60A, 494 (1969)
L. Bertocchi, S. Fubini, and M. Tonin, Nuovo Cimento 25, 626 (1962) D. Amati, A. Stanghellini, and S. Fubini, ibid. 26, 6 (1962)
G. F. Chew and A. Pignotti, Phys. Rev. Letters 20, 1078 (1968) Phys. Rev. 176, 2112 (1968)
G. F. Chew and C. DeTar, Phys. Rev. 180, 1577 (1969)
G. F. Chew and W. R. Frazer, Phys. Rev. 181, 1914 (1969)
M. Ciafaloni, C. DeTar, and M. Misheloff, Phys. Rev. 188, 2522 (1969) M. Ciafaloni and C. DeTar, Phys. Rev. D 1, 2917 (1970)
M. L. Goldberger, C.-I Tan, and J. M. Wang, Phys. Rev. 184, 1920 (1969) D. Silverman and C.-I Tan, Phys. Rev. D 1, 3479 (1970)
L. Caneschi and A. Pignotti, Phys. Rev. 180, 1525 (1969) Phys. Rev. Letters 22, 1219 (1969) D. M. Tow, Phys. Rev. D 2, 154 (1970) P. D. Ting, ibid. 2, 2982 (1970)
G. F. Chew, T. Rogers, and D. R. Snider, Phys. Rev. D 2, 765 (1970) G. F. Chew and D. R. Snider, ibid. 1, 3453 (1970)
S. Pinsky and W. I. Weisberger, Phys. Rev. D 2, 1640 (1970) ibid.2, 2365 (1970) H. D. I. Abarbanel and L. M. Saunders, ibid. 2, 711 (1970) A. H. Mueller and I. J. Muzinich, Ann. Phys. (N.Y.) 57, 20 (1970) ibid.57, 500 (1970)
G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961)
G. F. Chew, S-Matrix Theory of Strong Interactions (Benjamin, New York, 1962) G. F. ChewThe Analytic S-Matrix (Benjamin, New York, 1966) R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge Univ. Press, Cambridge, England, 1966)
T. W. B. Kibble, Phys. Rev. 131, 2282 (1963) R. G. Roberts and G. M. Frazer, ibid. 159, 1297 (1967) J. B. Hartle and C. E. Jones, ibid. 184, 1564 (1969)
M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959) G. C. Wick, ibid. 18, 65 (1962)
A. J. Macfarlane, J. Math. Phys. 4, 490 (1963)
N. F. Bali, G. F. Chew, and A. Pignotti, Phys. Rev. 163, 1572 (1967)
J. F. Boyce, J. Math. Phys. 8, 675 (1967) K.-H. Wang, Phys. Rev. D 1, 1754 (1970)
M. N. Misheloff, Phys. Rev. 184, 1732 (1969)
J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964) J. J. Jauch and F. Rohrlich, The Theory of Photon and Electrons (Addison-Wesley, Reading, Mass., 1955)
Omitted endnote
Omitted endnote
A. C. Aitken, Determinants and Matrices (Oliver and Boyd, London, 1939), p. 103
N. Byers and C. N. Yang, Rev. Mod. Phys. 36, 595 (1964)
E. P. Wigner, Ann. Math. 40, 149 (1939) in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Gürsey (Gordon and Breach, New York, 1964)
Omitted endnote
Omitted endnote
[14]
Omitted endnote
Omitted endnote
Omitted endnote
T. L. Trueman and G. C. Wick, Ann. Phys. (N.Y.) 26, 322 (1964) I. J. Muzinich, J. Math. Phys. 5, 1481 (1964) G. Cohen-Tannoudji, A. Morel, and H. Navelet, Ann. Phys. (N.Y.) 46, 239 (1968)
A. Capella, Nuovo Cimento 50A, 701 (1968) C. K. Chen and K.-H. Wang, Phys. Rev. 183, 1312 (1969)
A. McKerrell, Nuovo Cimento 34, 1289 (1964)
Omitted endnote
S. Mandelstam, Phys. Rev. 140, B375 (1965)
Omitted endnote
L. L. Chau Wang, Phys. Rev. 142, 1187 (1966)
M. Froissart, Phys. Rev. 123, 1053 (1961)

[c1] G. F. Chew, M. L. Goldberger, and F. E. Low, Phys. Rev. Letters 22, 208 (1969)

[c2] I. G. Halliday, Nuovo Cimento 60A, 177 (1969) I. G. Halliday and L. M. Saunders, ibid. 60A, 494 (1969)

[c3] L. Bertocchi, S. Fubini, and M. Tonin, Nuovo Cimento 25, 626 (1962) D. Amati, A. Stanghellini, and S. Fubini, ibid. 26, 6 (1962)

[c4] G. F. Chew and A. Pignotti, Phys. Rev. Letters 20, 1078 (1968) Phys. Rev. 176, 2112 (1968)

[c5] G. F. Chew and C. DeTar, Phys. Rev. 180, 1577 (1969)

[c6] G. F. Chew and W. R. Frazer, Phys. Rev. 181, 1914 (1969)

[c7] M. Ciafaloni, C. DeTar, and M. Misheloff, Phys. Rev. 188, 2522 (1969) M. Ciafaloni and C. DeTar, Phys. Rev. D 1, 2917 (1970)

[c8] M. L. Goldberger, C.-I Tan, and J. M. Wang, Phys. Rev. 184, 1920 (1969) D. Silverman and C.-I Tan, Phys. Rev. D 1, 3479 (1970)

[c9] L. Caneschi and A. Pignotti, Phys. Rev. 180, 1525 (1969) Phys. Rev. Letters 22, 1219 (1969) D. M. Tow, Phys. Rev. D 2, 154 (1970) P. D. Ting, ibid. 2, 2982 (1970)

[c10] G. F. Chew, T. Rogers, and D. R. Snider, Phys. Rev. D 2, 765 (1970) G. F. Chew and D. R. Snider, ibid. 1, 3453 (1970)

[c11] S. Pinsky and W. I. Weisberger, Phys. Rev. D 2, 1640 (1970) ibid.2, 2365 (1970) H. D. I. Abarbanel and L. M. Saunders, ibid. 2, 711 (1970) A. H. Mueller and I. J. Muzinich, Ann. Phys. (N.Y.) 57, 20 (1970) ibid.57, 500 (1970)

[c12] G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961)

[c13] G. F. Chew, S-Matrix Theory of Strong Interactions (Benjamin, New York, 1962) G. F. ChewThe Analytic S-Matrix (Benjamin, New York, 1966) R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge Univ. Press, Cambridge, England, 1966)

[c14] T. W. B. Kibble, Phys. Rev. 131, 2282 (1963) R. G. Roberts and G. M. Frazer, ibid. 159, 1297 (1967) J. B. Hartle and C. E. Jones, ibid. 184, 1564 (1969)

[c15] M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959) G. C. Wick, ibid. 18, 65 (1962)

[c16] A. J. Macfarlane, J. Math. Phys. 4, 490 (1963)

[c17] N. F. Bali, G. F. Chew, and A. Pignotti, Phys. Rev. 163, 1572 (1967)

[c18] J. F. Boyce, J. Math. Phys. 8, 675 (1967) K.-H. Wang, Phys. Rev. D 1, 1754 (1970)

[c19] M. N. Misheloff, Phys. Rev. 184, 1732 (1969)

[c20] J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964) J. J. Jauch and F. Rohrlich, The Theory of Photon and Electrons (Addison-Wesley, Reading, Mass., 1955)

[c21] Omitted endnote

[c22] Omitted endnote

[c23] A. C. Aitken, Determinants and Matrices (Oliver and Boyd, London, 1939), p. 103

[c24] N. Byers and C. N. Yang, Rev. Mod. Phys. 36, 595 (1964)

[c25] E. P. Wigner, Ann. Math. 40, 149 (1939) in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Gürsey (Gordon and Breach, New York, 1964)

[c26] Omitted endnote

[c27] Omitted endnote

[c28] [14]

[c29] Omitted endnote

[c30] Omitted endnote

[c31] Omitted endnote

[c32] T. L. Trueman and G. C. Wick, Ann. Phys. (N.Y.) 26, 322 (1964) I. J. Muzinich, J. Math. Phys. 5, 1481 (1964) G. Cohen-Tannoudji, A. Morel, and H. Navelet, Ann. Phys. (N.Y.) 46, 239 (1968)

[c33] A. Capella, Nuovo Cimento 50A, 701 (1968) C. K. Chen and K.-H. Wang, Phys. Rev. 183, 1312 (1969)

[c34] A. McKerrell, Nuovo Cimento 34, 1289 (1964)

[c35] Omitted endnote

[c36] S. Mandelstam, Phys. Rev. 140, B375 (1965)

[c37] Omitted endnote

[c38] L. L. Chau Wang, Phys. Rev. 142, 1187 (1966)

[c39] M. Froissart, Phys. Rev. 123, 1053 (1961)

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Partial-Wave Production Amplitudes and the Diagonalization of the Unitarity Relations in the Helicity Formalism

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