Hadron Electrodynamics in the Resonance Model: Deep-Inelastic <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>−</mo><mi>p</mi></math></span> Scattering, <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>−</mo><mi>e</mi></math></span> Colliding-Beam Processes, and Other Applications

Jamal T. Manassah; Satoshi Matsuda

doi:10.1103/PhysRevD.4.882

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Hadron Electrodynamics in the Resonance Model: Deep-Inelastic $e - p$ Scattering, $e - e$ Colliding-Beam Processes, and Other Applications

Jamal T. Manassah^* and Satoshi Matsuda

Institute for Advanced Study, Princeton, New Jersey 08540

^*Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 70-1866.

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Phys. Rev. D 4, 882 – Published 1 August, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.882

Abstract

Within the framework of the resonance model, we construct a well-defined gauge-invariant electromagnetic interaction for the composite hadrons, and we give the rules for the propagator and the current. We apply our formalism to deep-inelastic $e - p$ scattering, and we find that (a) the structure functions $W_{1}$ and $ν W_{2}$ scale and (b) the theoretical and experimental curves agree remarkably well for $ω > 1.5$ . We also predict the photoabsorption cross section to within 10% of the experimental value. In the colliding-beam processes, we find that (a) the structure functions for $e^{+} + e^{-} \to p +$ "anything" are connected with $W_{1}$ and $W_{2}$ , (b) the cross section for $e^{+} + e^{-} \to$ "anything" is larger than that for $e^{+} + e^{-} \to μ^{+} + μ^{-}$ , and it decreases as $s^{- 2}$ for large $s$ , and (c) the hadronic correction for the $ee \to ee π^{+} π^{-}$ rate is appreciable. We then present preliminary results on extending our work to include weak interactions, and we prove a structural theorem on the form of the currents. All the results in the paper are derived analytically.

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[c1] Selected Papers on Quantum Electrodynamics, edited by J. Schwinger (Dover, New York, 1958)

[c2] M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964)

[c3] S. L. Adler and R. F. Dashen, Current Algebras (Benjamin, New York, 1968)

[c4] J. J. Sakurai, Phys. Rev. Letters 22, 981 (1969) C. F. Cho and J. J. Sakurai, Phys. Letters 31B, 22 (1970)

[c5] R. C. Brower and J. H. Weis, Nuovo Cimento 65A, 654 (1970) P. V. Landshoff and J. C. Polkinghorne, Nucl. Phys. B19, 432 (1970) H. B. Nielsen and P. Olesen, CERN Report No. CERN-TH-1166, 1970 (unpublished)

[c6] R. P. Feynman, Phys. Rev. Letters 23, 1416 (1969) in Third International Conference on High-Energy Collisions, Stony Brook, 1969, edited by C. N. Yang (Gordon and Breach, New York, 1969), p. 237 J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969)

[c7] E. D. Bloom et al., the Fifteenth International Conference on High-Energy Physics, Kiev, U.S.S.R., 1970 [SLAC Report No. SLAC-PUB-796 (unpublished)]

[c8] D. O. Caldwell et al., in Proceedings of the Third International Conference on High-Energy Physics and Nuclear Structure, 1969, edited by S. Devons (Plenum, New York, 1970)

[c9] the Fifteenth International Conference on High-Energy Physics, Kiev, U.S.S.R., 1970 (unpublished)

[c10] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c11] J. D. Bjorken, Phys. Rev. 179, 1547 (1969)

[c12] Y. Nambu, in Symmetries and Quark Models, edited by R. Chand (Gordon and Breach, New York, 1970), p. 269 Y. Nambuthe Copenhagen Summer Symposium, 1970 (private communication) Y. Nambuseminar at the Institute for Advanced Study, 1970 L. Susskind, Phys. Rev. D 1, 1182 (1970) Nuovo Cimento 69, 457 (1970)

[c13] A. A. Logunov, L. D. Soloviev, and A. N. Tavkhelidze, Phys. Letters 24B, 181 (1967) K. Igi and S. Matsuda, Phys. Rev. Letters 18, 625 (1967) R. Dolen, D. Horn, and C. Schmid, Phys. Rev. 166, 1768 (1968)

[c14] G. Veneziano, Nuovo Cimento 57A, 190 (1968) M. Suzuki (private communication)

[c15] K. Bardakci and S. Mandelstam, Phys. Rev. 184, 1640 (1969) S. Fubini and G. Veneziano, Nuovo Cimento 64A, 811 (1969)

[c16] S. Fubini, D. Gordon, and G. Veneziano, Phys. Letters 29B, 679 (1969)

[c17] Y. Nambu, Progr. Theoret. Phys. (Kyoto) 5, 82 (1950) J. Schwinger, Phys. Rev. 82, 664 (1951) R. P. Feynman, ibid. 80, 440 (1950)

[c18] H. B. Nielsen and L. Susskind, Nucl. Phys. B28, 34 (1971)

[c19] L. N. Chang, P. G. O. Freund, and Y. Nambu, Phys. Rev. Letters 24, 628 (1970)

[c20] S. D. Drell, D. J. Levy, and T. M. Yan, Phys. Rev. D 1, 1617 (1970)

[c21] S. J. Brodsky, T. Kinoshita, and H. Terazawa, Phys. Rev. Letters 25, 972 (1970) V. E. Balakin, V. M. Budnev, and I. F. Ginzburg, Zh. Eksperim. i Teor. Fiz. Pis'ma v Redaktsiyu 11, 559 (1970) [Soviet Phys. JETP Letters 11, 388 (1970)]

[c22] R. Hagedorn, Nuovo Cimento 56A, 1027 (1968)

[c23] K. Kikkawa and H. Sato, Phys. Letters 32B, 280 (1970)

[c24] Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)

[c25] G. Domokos, S. Kovesi-Domokos, and E. Schonberg, Phys. Rev. D 3, 1184 (1971)

[c26] C. Callan and D. Gross, Phys. Rev. Letters 22, 156 (1969)

[c27] Y. Nambu and A. Hacinliyan, University of Chicago Report No. EFI 70-67 (unpublished)

[c28] M. Damashek and F. J. Gilman, Phys. Rev. D 1, 1319 (1970)

[c29] N. Cabibbo and R. Gatto, Phys. Rev. 124, 1577 (1961)

[c30] J. Dooher, Phys. Rev. Letters 19, 600 (1967) M. B. Halpern and G. Segrè, ibid. 19, 611 (1967)

[c31] R. B. Curtis, Phys. Rev. 104, 211 (1956) R. H. Dalitz and D. R. Yennie, ibid. 105, 1598 (1957)

[c32] J. T. Manassah and Satoshi Matsuda, Phys. Letters B (to be published) IAS report, 1971 (unpublished)

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Hadron Electrodynamics in the Resonance Model: Deep-Inelastic $e - p$ Scattering, $e - e$ Colliding-Beam Processes, and Other Applications

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Hadron Electrodynamics in the Resonance Model: Deep-Inelastic e−p Scattering, e−e Colliding-Beam Processes, and Other Applications

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References (32)

Hadron Electrodynamics in the Resonance Model: Deep-Inelastic $e - p$ Scattering, $e - e$ Colliding-Beam Processes, and Other Applications