Some Applications of a Simple Approach to Unitarization in Hard-Meson Calculations

Ronald Rockmore

doi:10.1103/PhysRevD.2.593

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Some Applications of a Simple Approach to Unitarization in Hard-Meson Calculations

Ronald Rockmore

Department of Physics, Rutgers-The State University, New Brunswick, New Jersey 08903

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Phys. Rev. D 2, 593 – Published 1 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.593

Abstract

Several applications of a simple approach to unitarization in the case of the three-point functions of hard-meson theory are made. For the first of these, effective-range formulas are obtained for the pion form factor in the timelike region for both hard-pion current-algebra ( $δ = - \frac{1}{2}$ ) and Veneziano models. Next, the extension of this procedure to the case of several coupled channels is used to obtain an effective-range formula for the pion form factor which includes the small effect of the closed $K \bar{K}$ channel. Finally, an expression for the pion form factor is derived which allows for the inclusion of some nonresonant $p$ -wave ( $I = 1$ ) $π π$ scattering. Since this component is parametrized via the introduction of an additional (nonresonant) $p$ -wave scattering length, the resulting expression for the pion form factor generates a one-parameter family of fits to the experimental data. The data appear to be consistent with a small positive nonresonant scattering length and favor a value of $Γ_{ρ}$ slightly less than 124 MeV.

References (18)

R. Rockmore, Phys. Rev. Letters 24, 541 (1970)
J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 23, 666 (1969)
H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)
[1–3] Sec. II
[1]
Omitted endnote
H. Suura, Phys. Rev. Letters 23, 551 (1969) ibid.23, 1007 (E) (1969)
[2] V. L. Auslander et al., Phys. Letters 25B, 433 (1967) Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968 (CERN, Geneva, 1968) J. E. Augustin et al., Phys. Letters 28B, 508 (1968)
Y. Ueda, Phys. Rev. 174, 2082 (1968)
Omitted endnote
Omitted endnote
I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 175, 1876 (1968)
S. Okubo and V. S. Mathur, Phys. Rev. Letters 23, 1412 (1969)
K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)
[2]
R. Arnowitt, M. H. Friedman, P. Nath, and R. Suitor, Phys. Rev. Letters 20, 475 (1968)
R. Rockmore, Phys. Rev. 151, 1228 (1966)
S. G. Brown and G. B. West, Phys. Rev. 168, 1605 (1968)

[c1] R. Rockmore, Phys. Rev. Letters 24, 541 (1970)

[c2] J. J. Brehm, E. Golowich, and S. C. Prasad, Phys. Rev. Letters 23, 666 (1969)

[c3] H. J. Schnitzer and S. Weinberg, Phys. Rev. 164, 1828 (1967)

[c4] [1–3] Sec. II

[c5] [1]

[c6] Omitted endnote

[c7] H. Suura, Phys. Rev. Letters 23, 551 (1969) ibid.23, 1007 (E) (1969)

[c8] [2] V. L. Auslander et al., Phys. Letters 25B, 433 (1967) Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968 (CERN, Geneva, 1968) J. E. Augustin et al., Phys. Letters 28B, 508 (1968)

[c9] Y. Ueda, Phys. Rev. 174, 2082 (1968)

[c10] Omitted endnote

[c11] Omitted endnote

[c12] I. S. Gerstein and H. J. Schnitzer, Phys. Rev. 175, 1876 (1968)

[c13] S. Okubo and V. S. Mathur, Phys. Rev. Letters 23, 1412 (1969)

[c14] K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)

[c15] [2]

[c16] R. Arnowitt, M. H. Friedman, P. Nath, and R. Suitor, Phys. Rev. Letters 20, 475 (1968)

[c17] R. Rockmore, Phys. Rev. 151, 1228 (1966)

[c18] S. G. Brown and G. B. West, Phys. Rev. 168, 1605 (1968)

Physical Review D

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Some Applications of a Simple Approach to Unitarization in Hard-Meson Calculations

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