Regge Slopes and Residues for a Spin-1 + Spin-0 System in the Content of <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo>(</mo><mn>4</mn><mo>)</mo><mn></mn></math></span> Symmetry and Bethe-Salpeter Model

Muhsin A. R. Abo-Shaeer

doi:10.1103/PhysRevD.2.2397

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Regge Slopes and Residues for a Spin-1 + Spin-0 System in the Content of $O (4)$ Symmetry and Bethe-Salpeter Model

Muhsin A. R. Abo-Shaeer^*

Department of Physics, University of California, Santa Barbara, California 93106

^*Present address: International Centre for Theoretical Physics, Trieste, Italy.

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Phys. Rev. D 2, 2397 – Published 15 November, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.2397

Abstract

The Bethe-Salpeter equation for a spin-1 + spin-0 system at vanishing total 4-momentum $K$ is separated by means of the $O (4)$ vector spherical harmonics, which are defined and discussed briefly. Perturbation expressions for the $M = 1$ residues near $K = 0$ are derived and then examined near $J = 0$ , where it is found that only the nonsense part of the $O (3)$ content of the $M = 1$ residues survives. Perturbation expressions are given also for the slopes of Regge trajectories at $s = - K^{2} = 0$ , the signs of the slopes are investigated for certain classes of potentials, and a sum rule satisfied by slopes of contiguous daughters is derived.

References (16)

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G. Domokos and P. Suranyi (unpublished)
R. F. Sawyer, Phys. Rev. 167, 1372 (1968)

[c1] G. Domokos and P. Suranyi, Nucl. Phys. 54, 529 (1964)

[c2] D. Z. Freedman and J. M. Wang, Phys. Rev. Letters 17, 569 (1966) Phys. Rev. 153, 1596 (1967)

[c3] M. Toller, Nuovo Cimento 53, 671 (1968)

[c4] S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper & Row, New York, 1962)

[c5] G. Domokos, Phys. Rev. 159, 1387 (1967)

[c6] W. R. Frazer, F. R. Halpern, H. M. Lipinski, and D. R. Snider, Phys. Rev. 176, 2047 (1968) H. M. Lipinski and D. R. Snider, ibid. 179, 1315 (1969)

[c7] A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U. P., Princeton, N. J., 1957)

[c8] M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1958)

[c9] R. Sawyer, Phys. Rev. Letters 19, 137 (1967)

[c10] S. Mandelstam, Phys. Rev. 168, 1884 (1968)

[c11] R. Sugar and R. Blankenbecler, Phys. Rev. Letters 20, 1014 (1968)

[c12] G. C. Wick, Phys. Rev. 96, 1124 (1954)

[c13] G. C. WickJ. Math. Phys. 11, 2272 (1970)

[c14] W. R. Frazer, F. R. Halpern, H. M. Lipinski, and D. R. Snider, Phys. Rev. 176, 2047 (1969)

[c15] G. Domokos and P. Suranyi (unpublished)

[c16] R. F. Sawyer, Phys. Rev. 167, 1372 (1968)

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Regge Slopes and Residues for a Spin-1 + Spin-0 System in the Content of $O (4)$ Symmetry and Bethe-Salpeter Model

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Regge Slopes and Residues for a Spin-1 + Spin-0 System in the Content of O(4) Symmetry and Bethe-Salpeter Model

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References (16)

Regge Slopes and Residues for a Spin-1 + Spin-0 System in the Content of $O (4)$ Symmetry and Bethe-Salpeter Model