Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors

Marcus T. Grisaru; Howard J. Schnitzer; Hung-Sheng Tsao

doi:10.1103/PhysRevD.8.4498

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Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors

Marcus T. Grisaru, Howard J. Schnitzer^*, and Hung-Sheng Tsao^*

Department of Physics, Brandeis University, Waltham, Massachusetts 02154

^*Work supported in part by the U. S. Atomic Energy Commission under Contract No. AT(11-1)3230.

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Phys. Rev. D 8, 4498 – Published 15 December, 1973

DOI: https://doi.org/10.1103/PhysRevD.8.4498

Abstract

The question of the Reggeization of the elementary particles in renormalizable gauge theories with the Higgs-Kibble mechanism is examined. It is concluded that the massive non-Abelian gauge vector mesons and $J = \frac{1}{2}$ fermions of these theoreis lie on Regge trajectories in every case in which a counting criterion due to Mandelstam is satisfied. Several explicit examples are presented which verify that the necessary factorization condition of the Born helicity matrices is satisfied at $J = 1$ and $J = \frac{1}{2}$ , supporting this conclusion.

References (20)

M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, Phys. Rev. 133, B145 (1964) M. Gell-Mann, M. L. Goldberger, F. E. Low, V. Singh, and F. Zachariasen, ibid. 133, B161 (1964) H. Cheng and T. T. Wu, ibid. 140, B465 (1965)
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S. Mandelstam, Phys. Rev. 137, B949 (1965)
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M. T. Grisaru, H. J. Schnitzer, and H.-S. Tsao [Phys. Rev. Lett. 30, 811 (1973)] H. J. Schnitzer, Ann. N. Y. Acad. Sci. (to be published) G. 't Hooft ([7])
Omitted endnote
M. T. Grisaru, H. J. Schnitzer, and H.-S. Tsao (unpublished)
B. W. Lee and J. Zinn-Justin, Phys. Rev. D 5, 3137 (1972) K. Barndakçi and M. B. Halpern, ibid. 6, 696 (1972) I. Bars, M. B. Halpern, and M. Yoshimura, Phys. Rev. Lett. 29, 969 (1972) Phys. Rev. D 7, 1233 (1973) K. Bardakçi, Nucl. Phys. B51, 174 (1973)
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D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972)
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[c1] M. Gell-Mann, M. L. Goldberger, F. E. Low, E. Marx, and F. Zachariasen, Phys. Rev. 133, B145 (1964) M. Gell-Mann, M. L. Goldberger, F. E. Low, V. Singh, and F. Zachariasen, ibid. 133, B161 (1964) H. Cheng and T. T. Wu, ibid. 140, B465 (1965)

[c2] P. G. Federbush and M. T. Grisaru, Ann. Phys. (N.Y.) 22, 263 (1963) ibid.22, 299 (1963) J. C. Polkinghorne, J. Math. Phys. 4, 503 (1963) R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge Univ. Press, New York, 1966)

[c3] S. Mandelstam, Phys. Rev. 137, B949 (1965)

[c4] E. Abers and V. L. Teplitz, Phys. Rev. 158, 1365 (1967)

[c5] D. A. Dicus, D. Z. Freedman, and V. L. Teplitz, Phys. Rev. D 4, 2320 (1971)

[c6] E. Abers, R. A. Keller, and V. L. Teplitz, Phys. Rev. D 2, 1757 (1970)

[c7] S. Weinberg, Phys. Rev. Lett. 13, 1264 (1967) A. Salam, in Elementary Particle Theory, edited by N. Svartholm (Almquist, Stockholm, 1968) G. 't Hooft, Nucl. Phys. B35, 167 (1971) B. W. Lee, Phys. Rev. D 5, 823 (1972) B. W. Lee and J. Zinn-Justin, ibid. 5, 3121 (1972) ibid.5, 3137 (1972) ibid.5, 3155 (1972)

[c8] A. Neveu and J. Scherk, Nucl. Phys. B36, 155 (1972) ibid.B36, 317 (1972) J. L. Gervais and A. Neveu, ibid. B46, 381 (1972) J. Scherk, ibid. B31, 222 (1971)

[c9] M. T. Grisaru, H. J. Schnitzer, and H.-S. Tsao [Phys. Rev. Lett. 30, 811 (1973)] H. J. Schnitzer, Ann. N. Y. Acad. Sci. (to be published) G. 't Hooft ([7])

[c10] Omitted endnote

[c11] M. T. Grisaru, H. J. Schnitzer, and H.-S. Tsao (unpublished)

[c12] B. W. Lee and J. Zinn-Justin, Phys. Rev. D 5, 3137 (1972) K. Barndakçi and M. B. Halpern, ibid. 6, 696 (1972) I. Bars, M. B. Halpern, and M. Yoshimura, Phys. Rev. Lett. 29, 969 (1972) Phys. Rev. D 7, 1233 (1973) K. Bardakçi, Nucl. Phys. B51, 174 (1973)

[c13] M. Veltman (unpublished) D. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972) C. Bouchiat, J. Iliopoulos, and Ph. Meyer, Phys. Lett. 42B, 91 (1972) H. Georgi and S. L. Glashow, Phys. Rev. D 6, 429 (1972) W. A. Bardeen, in Proceedings of the XVI International Conference on High Energy Physics, Chicago-Batavia, Ill., 1972, edited by J. D. Jackson and A. Roberts (NAL, Batavia, Ill., 1973), Vol. 2, p. 295 S. L. Alder, in Brandeis University Lectures in Theoretical Physics, edited by S. Deser, M. Grisaru, and H. Pendelton (MIT Press, Cambridge, Mass., 1970) R. Jackiw, in S. Treiman, R. Jackiw, and D. J. Gross, Lectures on Current Algebra and its Applications (Princeton Univ. Press, Princeton, N. J., 1972)

[c14] D. J. Gross and R. Jackiw, Phys. Rev. D 6, 477 (1972)

[c15] P. W. Higgs, Phys. Lett. 12, 132 (1964) Phys. Rev. Lett. 13, 508 (1964) Phys. Rev. 145, 1156 (1966) G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964) T. W. B. Kibble, Phys. Rev. 155, 1554 (1967) F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964)

[c16] M. T. Grisaru and H.-S. Tsao, Phys. Rev. D (to be published)

[c17] D. A. Dicus and V. L. Teplitz, Phys. Rev. D 3, 1910 (1971)

[c18] S. Weinberg, Phys. Rev. Lett. 27, 1688 (1971) H. R. Quinn (unpublished) as reported by B. W. Lee, in Proceedings of the XVI International Conference on High Energy Physics, Chicago-Batavia, Ill., 1972, edited by J. D. Jackson and A. Roberts (NAL, Batavia, Ill., 1973), Vol. 4, p. 249 (especially the appendix to sec. 2) J. Cornwall, D. Levin, and G. Tiktopoulos, Phys. Rev. Lett. 30, 1268 (1973) ibid.31, 572(E) (1973) J. S. Bell, CERN Report No. Th-1669, 1973 (unpublished) C. H. Llewellyn Smith, Phys. Lett. 46B, 233 (1973)

[c19] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965), Vol. II

[c20] M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959)

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Reggeization of Elementary Particles in Renormalizable Gauge Theories: Vectors and Spinors

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