Deep-Inelastic <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>e</mi><mo>−</mo><mi></mi><mi>p</mi></math></span> Structure Functions in a Ladder Model with Spin-½ Nucleons

Stephen Blaha

doi:10.1103/PhysRevD.3.510

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Deep-Inelastic $e - p$ Structure Functions in a Ladder Model with Spin-½ Nucleons

Stephen Blaha

The Rockefeller University, New York, New York 10021

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Phys. Rev. D 3, 510 – Published 15 January, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.510

Abstract

We find the asymptotic behavior of the inelastic electron-proton structure functions $W_{1}$ and $W_{2}$ in the limit $| q^{2} | \to \infty$ with $ω = \frac{2 q \cdot p}{| q^{2} |}$ fixed ( $q$ is the electron four-momentum transfer and $p$ the target nucleon four-momentum) using a ladder model for the virtual Compton amplitude. Neutral vector mesons are exchanged between the (spin-½) proton legs. In addition, this model (with slight modifications) gives the asymptotic behavior for a ladder model in which pseudoscalar mesons are exchanged, and the asymptotic behavior for a truss-bridge-graph model in a mixed $φ^{3} - φ^{4}$ field theory. In all of these models $W_{1}$ and $ν W_{2}$ do not scale because of factors of $\ln | q^{2} |$ (with the exception of $ν W_{2}$ in the truss-bridge model). In addition, we find that the structure functions are essentially Bessel functions with the argument $\ln | q^{2} | \ln ω$ in the $| q^{2} | \to \infty$ limit for fixed $ω ≫ 1$ .

References (13)

H. D. I. Abarbanel, M. L. Goldberger, and S. B. Treiman, Phys. Rev. Letters 22, 500 (1969)
G. Altarelli and H. R. Rubinstein, Phys. Rev. 187, 2111 (1969)
J. D. Bjorken and T. T. Wu, Phys. Rev. 130, 2566 (1963)
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S. D. Drell and J. D. Walecka, Ann. Phys. (N. Y.) 28, 18 (1964)
S. J. Chang and P. M. Fishbane, Phys. Rev. D 2, 1084 (1970)
R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge U. P., New York, 1966), pp. 151-154
[4], p. 312
[4], p. 308
S. Adler and Wu-ki Tung, Phys. Rev. Letters 22, 978 (1969) R. Jackiw and G. Preparata, ibid. 22, 975 (1969)
S. D. Drell, D. J. Levy, and T. Yan, Phys. Rev. Letters 22, 744 (1969)
[7], pp. 34-36
M. Hamermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962), p. 25

[c1] H. D. I. Abarbanel, M. L. Goldberger, and S. B. Treiman, Phys. Rev. Letters 22, 500 (1969)

[c2] G. Altarelli and H. R. Rubinstein, Phys. Rev. 187, 2111 (1969)

[c3] J. D. Bjorken and T. T. Wu, Phys. Rev. 130, 2566 (1963)

[c4] Bateman Manuscript Project, Tables of Integral Transforms, edited by A. Erdélyi (McGraw-Hill, New York, 1954), p. 371

[c5] S. D. Drell and J. D. Walecka, Ann. Phys. (N. Y.) 28, 18 (1964)

[c6] S. J. Chang and P. M. Fishbane, Phys. Rev. D 2, 1084 (1970)

[c7] R. J. Eden, P. V. Landshoff, D. I. Olive, and J. C. Polkinghorne, The Analytic S-Matrix (Cambridge U. P., New York, 1966), pp. 151-154

[c8] [4], p. 312

[c9] [4], p. 308

[c10] S. Adler and Wu-ki Tung, Phys. Rev. Letters 22, 978 (1969) R. Jackiw and G. Preparata, ibid. 22, 975 (1969)

[c11] S. D. Drell, D. J. Levy, and T. Yan, Phys. Rev. Letters 22, 744 (1969)

[c12] [7], pp. 34-36

[c13] M. Hamermesh, Group Theory (Addison-Wesley, Reading, Mass., 1962), p. 25

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Deep-Inelastic $e - p$ Structure Functions in a Ladder Model with Spin-½ Nucleons

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Deep-Inelastic e−p Structure Functions in a Ladder Model with Spin-½ Nucleons

Abstract

References (13)

Deep-Inelastic $e - p$ Structure Functions in a Ladder Model with Spin-½ Nucleons