Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results for <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ρ</mi><mo>−</mo><mi>π</mi></math></span> and <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>π</mi></math></span> Scattering

K. C. GUPTA; J. S. VAISHYA

doi:10.1103/PhysRev.178.2177

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Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results for $ρ - π$ and $A_{1} - π$ Scattering

K. C. GUPTA

J. S. VAISHYA

Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556

Theoretical Physics Division, National Physical Laboratory, and Department of Physics, University of Delhi, Delhi, India

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Phys. Rev. 178, 2177 – Published 25 February, 1969

DOI: https://doi.org/10.1103/PhysRev.178.2177

Abstract

Following recent attempts to explore possible connections between current algebra, dispersion relations, and Regge pole theory, we consider $ρ - π$ and $A_{1} - π$ scattering amplitudes, and calculate them both from the hard-pion current algebra for four-point functions and dispersion relations with saturation by single-particle intermediate states. The two are found to lead to mutually consistent results provided we introduce a subtraction in certain amplitudes. However, from Regge pole theory, many of these are found to require no subtractions. Thus, whereas the current algebra and the pole-dominated dispersion relations understandably give similar results, the Regge pole theory appears to give distinctly different results.

References (24)

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B. Renner, Current Algebra and Their Applications (Pergamon Press, Inc., London, 1968) S. Adler and R. Dashen, Current Algebras and Applications to Particle Physics (W. A. Benjamin, Inc., New York, 1968)
B. Renner, Phys. Letters 21, 143 (1966)
S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967) S. Okubo, in Proceedings of the International Conference on Particles and Fields, Rochester, 1967 (Wiley-Interscience Publishers, Inc., New York, 1967) S. G. Brown and G. B. West, Phys. Rev. Letters 19, 812 (1967)
[4,6]
S. Okubo et al., [4] T. Das, V. S. Mathur, and S. Okubo, Phys. Rev. Letters 19, 1067 (1967) H. T. Nieh, ibid. 21, 116 (1968)
H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967) I. S. Gerstein and H. J. Schnitzer, ibid. 170, 1638 (1968) K. C. Gupta and J. S. Vaishya, ibid. 170, 1530 (1968) I. S. Gerstein, H. J. Schnitzer, and S. Weinberg, ibid. 175, 1873 (1968)
K. Kawarabayashi, talk given at the Eleventh Boulder Conference, 1968 (unpublished) D. A. Geffen and S. Gasiorowicz, Argonne National Laboratory Report, 1968 (unpublished)
K. C. Gupta and J. S. Vaishya (to be published) R. Chanda, R. N. Mohapatra, and S. Okubo, Phys. Rev. 170, 1344 (1968)
R. J. N. Phillips, Phys. Letters 24B, 342 (1967) I. J. Muzinich, Phys. Rev. Letters 18, 381 (1967) V. de Alfaro, S. Fubini, G. Furlan, and C. Rossetti, Phys. Letters 21, 576 (1966) [23]
J. B. Bronzan, I. S. Gerstein, B. W. Lee, and F. E. Low, Phys. Rev. Letters 18, 32 (1967) V. Singh, ibid. 18, 36 (1967)
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[7]
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[7] [14]
S. Weinberg, Phys. Rev. Letters 18, 507 (1967) K. Kawarabayashi and M. Suzuki, ibid. 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966) J. J. Sakurai, Phys. Rev. Letters 19, 803 (1967)
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[c1] S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) Phys. Rev. 140, B736 (1965) W. I. Weisberger, Phys. Rev. Letters 14, 1047 (1965) Phys. Rev. 143, 1302 (1966)

[c2] B. Renner, Current Algebra and Their Applications (Pergamon Press, Inc., London, 1968) S. Adler and R. Dashen, Current Algebras and Applications to Particle Physics (W. A. Benjamin, Inc., New York, 1968)

[c3] B. Renner, Phys. Letters 21, 143 (1966)

[c4] S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967) S. Okubo, in Proceedings of the International Conference on Particles and Fields, Rochester, 1967 (Wiley-Interscience Publishers, Inc., New York, 1967) S. G. Brown and G. B. West, Phys. Rev. Letters 19, 812 (1967)

[c5] [4,6]

[c6] S. Okubo et al., [4] T. Das, V. S. Mathur, and S. Okubo, Phys. Rev. Letters 19, 1067 (1967) H. T. Nieh, ibid. 21, 116 (1968)

[c7] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967) I. S. Gerstein and H. J. Schnitzer, ibid. 170, 1638 (1968) K. C. Gupta and J. S. Vaishya, ibid. 170, 1530 (1968) I. S. Gerstein, H. J. Schnitzer, and S. Weinberg, ibid. 175, 1873 (1968)

[c8] K. Kawarabayashi, talk given at the Eleventh Boulder Conference, 1968 (unpublished) D. A. Geffen and S. Gasiorowicz, Argonne National Laboratory Report, 1968 (unpublished)

[c9] K. C. Gupta and J. S. Vaishya (to be published) R. Chanda, R. N. Mohapatra, and S. Okubo, Phys. Rev. 170, 1344 (1968)

[c10] R. J. N. Phillips, Phys. Letters 24B, 342 (1967) I. J. Muzinich, Phys. Rev. Letters 18, 381 (1967) V. de Alfaro, S. Fubini, G. Furlan, and C. Rossetti, Phys. Letters 21, 576 (1966) [23]

[c11] J. B. Bronzan, I. S. Gerstein, B. W. Lee, and F. E. Low, Phys. Rev. Letters 18, 32 (1967) V. Singh, ibid. 18, 36 (1967)

[c12] I. S. Gerstein and H. J. Schnitzer, [7]

[c13] [7]

[c14] R. Arnowitt, M. H. Friedman, P. Nath, and R. Suitor, Phys. Rev. Letters 20, 475 (1968) [7,8]

[c15] M. Gell-Mann and M. Lévy, Nuovo Cimento 16, 705 (1960) Y. Nambu, Phys. Rev. Letters 4, 380 (1960)

[c16] N. M. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967) J. J. Sakurai, Report No. EFINS 67-64 (unpublished)

[c17] [7] [14]

[c18] S. Weinberg, Phys. Rev. Letters 18, 507 (1967) K. Kawarabayashi and M. Suzuki, ibid. 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966) J. J. Sakurai, Phys. Rev. Letters 19, 803 (1967)

[c19] H. J. Schnitzer and S. Weinberg, [7]

[c20] S. N. Biswas, R. Dutt, and K. G. Gupta, Ann. Phys. (N. Y.) (to be published)

[c21] I. S. Gerstein and H. J. Schnitzer in [7]

[c22] D. A. Geffen and S. Gasiorowicz, [8]

[c23] F. J. Gilman and H. Harari, Phys. Rev. 165, 1803 (1968)

[c24] S. G. Brown and G. B. West, Phys. Rev. 174, 1786 (1968)

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Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results for $ρ - π$ and $A_{1} - π$ Scattering

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Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results for ρ−π and A1−π Scattering

Abstract

References (24)

Dispersion-Theoretic Approach to Hard-Pion Current-Algebra Results for $ρ - π$ and $A_{1} - π$ Scattering