Operator-Product Expansions, Neutrino Scattering, and the Dimension of the Symmetry-Breaking Hamiltonian

Stanley G. Brown

doi:10.1103/PhysRevD.5.2593

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Operator-Product Expansions, Neutrino Scattering, and the Dimension of the Symmetry-Breaking Hamiltonian

Stanley G. Brown

Department of Physics, University of California, Los Angeles, California 90024

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Phys. Rev. D 5, 2593 – Published 15 May, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.2593

Abstract

The structure functions $W_{4}$ and $W_{5}$ in inelastic neutrino-nucleon scattering are analyzed, using Wilson operator-product expansions. The $ν$ dependence of the structure functions in the Bjorken scaling limit is related to the dimensions ( $Δ_{i}$ ) of the terms in the SU (3) ⊗ SU (3)-breaking Hamiltonian. Restrictions due to positive definiteness are used. Several applications of the analysis are made: (1) If the axial-vector current behaves as a canonical pion field, then there must exist a field of dimension ≤0. (2) A "maximal-contribution assumption" implies that $Δ_{1}$ , the largest of the $Δ_{i}$ , is ≥2. (3) A proposed experimental determination of $Δ_{1}$ is analyzed. (4) Implications for internal-symmetry structure of the vanishing of $W_{L}$ are discussed.

References (21)

K. G. Wilson, Phys. Rev. 179, 1499 (1969)
S. G. Brown, Phys. Letters (to be published)
M. G. Doncel and E. de Rafael, Nuovo Cimento 4A, 363 (1971)
J. D. Bjorken, Phys. Rev. 179, 1547 (1969)
S. G. Brown, Phys. Rev. Letters 27, 347 (1971)
J. Mandula, A. Schwimmer, J. Weyers, and G. Zweig, Phys. Letters 37B, 109 (1971)
D. J. Gross and S. B. Treiman, Phys. Rev. D 4, 1059 (1971)
G. Mack, Nucl. Phys. B35, 592 (1971) Y. Frishman, Phys. Rev. Letters 25, 966 (1970) Ann. Phys. (N.Y.) 66, 373 (1971) Mandula et al., [6] B. W. Lee and J. E. Mandula, Phys. Rev. D 4, 3475 (1971)
Omitted endnote
I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1
R. Jackiw, R. Van Royen, and G. B. West, Phys. Rev. D 2, 2473 (1970)
Omitted endnote
[2]
M. Gell-Mann, in Proceedings of the Third Hawaii Topical Conference on Particle Physics, edited by S. F. Tuan (Western Periodicals, North Hollywood, Calif., 1969)
K. G. Wilson, Phys. Rev. D 3, 1818 (1971)
T. H. White, The Once and Future King (Putnam's Sons, New York, 1958), p. 121 O.-M. Bilaniuk and E. C. G. Sudarshan, Phys. Today 22, No. 5, 43 (1969) G. L. Trigg, ibid. 23, No. 10, 79 (1970)
P. Nath, R. Arnowitt, and M. H. Friedman, Northeastern University Report No. NUB 2091, 1971 (unpublished)
E. D. Bloom et al., MIT-SLAC Report No. SLAC-PUB-796, 1970 (unpublished) presented at the Fifteenth International Conference on High-Energy Physics, Kiev, U.S.S.R., 1970
Mack, [8]
Omitted endnote
C. G. Callan and D. J. Gross, Phys. Rev. Letters 22, 156 (1969)

[c1] K. G. Wilson, Phys. Rev. 179, 1499 (1969)

[c2] S. G. Brown, Phys. Letters (to be published)

[c3] M. G. Doncel and E. de Rafael, Nuovo Cimento 4A, 363 (1971)

[c4] J. D. Bjorken, Phys. Rev. 179, 1547 (1969)

[c5] S. G. Brown, Phys. Rev. Letters 27, 347 (1971)

[c6] J. Mandula, A. Schwimmer, J. Weyers, and G. Zweig, Phys. Letters 37B, 109 (1971)

[c7] D. J. Gross and S. B. Treiman, Phys. Rev. D 4, 1059 (1971)

[c8] G. Mack, Nucl. Phys. B35, 592 (1971) Y. Frishman, Phys. Rev. Letters 25, 966 (1970) Ann. Phys. (N.Y.) 66, 373 (1971) Mandula et al., [6] B. W. Lee and J. E. Mandula, Phys. Rev. D 4, 3475 (1971)

[c9] Omitted endnote

[c10] I. M. Gel'fand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1

[c11] R. Jackiw, R. Van Royen, and G. B. West, Phys. Rev. D 2, 2473 (1970)

[c12] Omitted endnote

[c13] [2]

[c14] M. Gell-Mann, in Proceedings of the Third Hawaii Topical Conference on Particle Physics, edited by S. F. Tuan (Western Periodicals, North Hollywood, Calif., 1969)

[c15] K. G. Wilson, Phys. Rev. D 3, 1818 (1971)

[c16] T. H. White, The Once and Future King (Putnam's Sons, New York, 1958), p. 121 O.-M. Bilaniuk and E. C. G. Sudarshan, Phys. Today 22, No. 5, 43 (1969) G. L. Trigg, ibid. 23, No. 10, 79 (1970)

[c17] P. Nath, R. Arnowitt, and M. H. Friedman, Northeastern University Report No. NUB 2091, 1971 (unpublished)

[c18] E. D. Bloom et al., MIT-SLAC Report No. SLAC-PUB-796, 1970 (unpublished) presented at the Fifteenth International Conference on High-Energy Physics, Kiev, U.S.S.R., 1970

[c19] Mack, [8]

[c20] Omitted endnote

[c21] C. G. Callan and D. J. Gross, Phys. Rev. Letters 22, 156 (1969)

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Operator-Product Expansions, Neutrino Scattering, and the Dimension of the Symmetry-Breaking Hamiltonian

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