Asymptotic Sum Rules for Three-Point Functions: the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mo>−</mo><mi>ρ</mi><mo>−</mo><mi>π</mi></math></span> System

V. S. Mathur

doi:10.1103/PhysRev.174.1743

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Asymptotic Sum Rules for Three-Point Functions: the $A_{1} - ρ - π$ System

V. S. Mathur

Department of Physics and Astronomy, University of Rochester, Rochester, New York

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Phys. Rev. 174, 1743 – Published 25 October, 1968

DOI: https://doi.org/10.1103/PhysRev.174.1743

Abstract

The $A_{1} - ρ - π$ system is studied and it is shown that the question of possible subtractions in the dispersion relations for form factors is crucial for understanding the difference between hard- and soft-pion results in the $A_{1}$ and $ρ$ decays. A double dispersion representation is suggested for three-point functions. Using a truncation approximation, the Bjorken technique is employed to derive several new sum rules for the spectral functions. Assuming that the sum rules are saturated by low-lying meson states, a study is made to evaluate the constant terms in the dispersion representations of the form factors involved in the $A_{1} ρ π$ and $ρ π π$ vertices. The case of no subtractions, which formally leads to the soft-pion results, is ruled out on the basis of this investigation, and the well-known hard-pion results for $A_{1}$ and $ρ$ decays are rederived.

References (26)

B. Renner, Phys. Letters 21, 453 (1966)
S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967)
J. Schwinger, Phys. Letters 24B, 473 (1967)
J. Wess and B. Zumino, Phys. Rev. 163, 1727 (1967)
F. J. Gilman and H. Harari, Phys. Rev. 165, 1803 (1968)
H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)
D. A. Geffen, Phys. Rev. Letters 19, 770 (1967)
S. G. Brown and G. B. West, Phys. Rev. Letters 19, 812 (1967) Phys. Rev. 168, 1605 (1968)
T. Das, V. S. Mathur, and S. Okubo, Phys. Rev. Letters 19, 1067 (1967)
R. Arnowitt, M. H. Friedman, and P. Nath, Phys. Rev. Letters 19, 1085 (1967)
D. S. Narayan, P. P. Srivastava, and R. P. Saxena, Phys. Rev. 167, 1379 (1968)
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H. T. Nieh, Phys. Rev. 163, 1769 (1967)
T. D. Lee, S. Weinberg, and B. Zumino, Phys. Rev. Letters 18, 1029 (1967)
R. P. Feynman, M. Gell-Mann, and G. Zweig, Phys. Rev. Letters 13, 678 (1964)
[9]
Omitted endnote
S. Weinberg, Phys. Rev. Letters 18, 507 (1967)
K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)
[9] [6]
Omitted endnote
[8]
Nieh ([13])
Omitted endnote
Omitted endnote
G. W. Barry and J. J. Sakurai, SLAC Report No. Pub-382 (unpublished)

[c1] B. Renner, Phys. Letters 21, 453 (1966)

[c2] S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967)

[c3] J. Schwinger, Phys. Letters 24B, 473 (1967)

[c4] J. Wess and B. Zumino, Phys. Rev. 163, 1727 (1967)

[c5] F. J. Gilman and H. Harari, Phys. Rev. 165, 1803 (1968)

[c6] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)

[c7] D. A. Geffen, Phys. Rev. Letters 19, 770 (1967)

[c8] S. G. Brown and G. B. West, Phys. Rev. Letters 19, 812 (1967) Phys. Rev. 168, 1605 (1968)

[c9] T. Das, V. S. Mathur, and S. Okubo, Phys. Rev. Letters 19, 1067 (1967)

[c10] R. Arnowitt, M. H. Friedman, and P. Nath, Phys. Rev. Letters 19, 1085 (1967)

[c11] D. S. Narayan, P. P. Srivastava, and R. P. Saxena, Phys. Rev. 167, 1379 (1968)

[c12] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c13] H. T. Nieh, Phys. Rev. 163, 1769 (1967)

[c14] T. D. Lee, S. Weinberg, and B. Zumino, Phys. Rev. Letters 18, 1029 (1967)

[c15] R. P. Feynman, M. Gell-Mann, and G. Zweig, Phys. Rev. Letters 13, 678 (1964)

[c16] [9]

[c17] Omitted endnote

[c18] S. Weinberg, Phys. Rev. Letters 18, 507 (1967)

[c19] K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)

[c20] [9] [6]

[c21] Omitted endnote

[c22] [8]

[c23] Nieh ([13])

[c24] Omitted endnote

[c25] Omitted endnote

[c26] G. W. Barry and J. J. Sakurai, SLAC Report No. Pub-382 (unpublished)

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Asymptotic Sum Rules for Three-Point Functions: the $A_{1} - ρ - π$ System

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Asymptotic Sum Rules for Three-Point Functions: the A1−ρ−π System

Abstract

References (26)

Asymptotic Sum Rules for Three-Point Functions: the $A_{1} - ρ - π$ System