Current Commutators and the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span> Nonet in Electroproduction and Neutrino-Induced Production

John M. Cornwall

doi:10.1103/PhysRevD.2.578

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Current Commutators and the $2^{+}$ Nonet in Electroproduction and Neutrino-Induced Production

John M. Cornwall^*

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

^*Alfred P. Sloan Foundation Fellow.

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Phys. Rev. D 2, 578 – Published 1 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.578

Abstract

Commutators of the type $[{\dot{J}}_{i}, J_{i}]$ , where $J_{μ}$ is a vector or an axial-vector current, are expressed in terms of canonical $2^{+}$ meson fields. (More generally, a commutator involving the $n$ th time derivative is expressed in terms of fields of spin $n + 1$ .) One consequence is that electromagnetic mass differences are finite. Predictions are made for electroproduction and neutrino-induced production; where comparisons are possible, the agreement with experiment is excellent.

References (25)

S. L. Adler and R. F. Dashen, Current Algebra (Benjamin, New York, 1968)
J. M. Cornwall and R. E. Norton, Phys. Rev. 177, 2584 (1969)
T. D. Lee, S. Weinberg, and B. Zumino, Phys. Rev. Letters 18, 1029 (1967)
H. Sugawara, Phys. Rev. 170, 1659 (1968)
J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969)
C. H. Llewellyn Smith, CERN Report No. TH. 1097, 1969 (unpublished)
D. J. Gross, Phys. Rev. Letters 21, 308 (1968) D. J. Gross and C. G. Callan, ibid. 21, 311 (1968)
[15]
S. L. Glashow and R. H. Socolow, Phys. Rev. Letters 15, 329 (1965)
J. D. Bjorken, Phys. Rev. 179, 1547 (1969)
S. Okubo, Phys. Letters 5, 165 (1963) H. Sugawara and F. von Hippel, Phys. Rev. 141, 1331 (1966)
V. Barger, M. Olsson, and K. V. L. Sarma, Phys. Rev. 147, 1115 (1966)
P. G. O. Freund, Phys. Letters 2, 136 (1962) ibid.16, 291 (1966) M. Gell-Mann, Phys. Rev. 125, 1067 (1962)
J. D. Bjorken, Phys. Rev. 148, 1467 (1966)
J. M. Cornwall and R. E. Norton, Phys. Rev. 173, 1637 (1968)
Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)
[2]
H. D. I. Abarbanel, M. Goldberger, and S. B. Treiman, Phys. Rev. Letters 22, 500 (1969) R. A. Brandt, ibid. 22, 1149 (1969) J. M. Cornwall and R. E. Norton (unpublished)
H. Harari, Phys. Rev. Letters 22, 1078 (1969)
J. M. Cornwall, D. Corrigan, and R. E. Norton, Phys. Rev. Letters 24, 1141 (1970)
E. D. Bloom et al., Phys. Rev. Letters 23, 930 (1969) M. Breidenbach et al., ibid. 23, 935 (1969)
I. Budagov et al., Phys. Letters 30B, 364 (1969)
R. F. Dashen and Y. Frishman, Phys. Rev. Letters 22, 572 (1969)
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G. Mack and A. Salam, Ann. Phys. (N. Y.) 53, 174 (1969) D. J. Gross and J. E. Wess, Phys. Rev. D (to be published) P. Carruthers and M. Gell-Mann (unpublished)

[c1] S. L. Adler and R. F. Dashen, Current Algebra (Benjamin, New York, 1968)

[c2] J. M. Cornwall and R. E. Norton, Phys. Rev. 177, 2584 (1969)

[c3] T. D. Lee, S. Weinberg, and B. Zumino, Phys. Rev. Letters 18, 1029 (1967)

[c4] H. Sugawara, Phys. Rev. 170, 1659 (1968)

[c5] J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969)

[c6] C. H. Llewellyn Smith, CERN Report No. TH. 1097, 1969 (unpublished)

[c7] D. J. Gross, Phys. Rev. Letters 21, 308 (1968) D. J. Gross and C. G. Callan, ibid. 21, 311 (1968)

[c8] [15]

[c9] S. L. Glashow and R. H. Socolow, Phys. Rev. Letters 15, 329 (1965)

[c10] J. D. Bjorken, Phys. Rev. 179, 1547 (1969)

[c11] S. Okubo, Phys. Letters 5, 165 (1963) H. Sugawara and F. von Hippel, Phys. Rev. 141, 1331 (1966)

[c12] V. Barger, M. Olsson, and K. V. L. Sarma, Phys. Rev. 147, 1115 (1966)

[c13] P. G. O. Freund, Phys. Letters 2, 136 (1962) ibid.16, 291 (1966) M. Gell-Mann, Phys. Rev. 125, 1067 (1962)

[c14] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c15] J. M. Cornwall and R. E. Norton, Phys. Rev. 173, 1637 (1968)

[c16] Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)

[c17] [2]

[c18] H. D. I. Abarbanel, M. Goldberger, and S. B. Treiman, Phys. Rev. Letters 22, 500 (1969) R. A. Brandt, ibid. 22, 1149 (1969) J. M. Cornwall and R. E. Norton (unpublished)

[c19] H. Harari, Phys. Rev. Letters 22, 1078 (1969)

[c20] J. M. Cornwall, D. Corrigan, and R. E. Norton, Phys. Rev. Letters 24, 1141 (1970)

[c21] E. D. Bloom et al., Phys. Rev. Letters 23, 930 (1969) M. Breidenbach et al., ibid. 23, 935 (1969)

[c22] I. Budagov et al., Phys. Letters 30B, 364 (1969)

[c23] R. F. Dashen and Y. Frishman, Phys. Rev. Letters 22, 572 (1969)

[c24] C. Bouchiat, J. Iliopoulos, and J. Prentki, Nuovo Cimento 56A, 1150 (1969)

[c25] G. Mack and A. Salam, Ann. Phys. (N. Y.) 53, 174 (1969) D. J. Gross and J. E. Wess, Phys. Rev. D (to be published) P. Carruthers and M. Gell-Mann (unpublished)

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Current Commutators and the $2^{+}$ Nonet in Electroproduction and Neutrino-Induced Production

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Current Commutators and the 2+ Nonet in Electroproduction and Neutrino-Induced Production

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References (25)

Current Commutators and the $2^{+}$ Nonet in Electroproduction and Neutrino-Induced Production