<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math></span>-Wave <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math></span> Scattering in the Effective-Potential Approximation

Allen E. Everett

doi:10.1103/PhysRevD.4.2797

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$S$ -Wave $π π$ Scattering in the Effective-Potential Approximation

Allen E. Everett

Department of Physics, Tufts University, Medford, Massachusetts 02155

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Phys. Rev. D 4, 2797 – Published 1 November, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.2797

Abstract

The $I = 0$ and $I = 2$ $π π$ $S$ -wave phase shifts are calculated, using the effective-potential model with $ρ$ and $f^{0}$ exchange which has yielded an earlier successful $ρ - f^{0}$ double bootstrap. Scattering lengths and a broad $S$ -wave resonance in fair qualitative agreement with current experimental indications are obtained. However, the $I = 0$ phase shift becomes negative between about 350 and 700 MeV, in disagreement with the dispersion-theory analysis of Morgan and Shaw and with current-algebra predictions on the energy derivative of the amplitude.

References (12)

D. Morgan and G. Shaw, Phys. Rev. D 2, 520 (1970)
S. Weinberg, Phys. Rev. Letters 17, 616 (1966)
A. E. Everett, Phys. Rev. 173, 1663 (1968)
P. D. P. Collins and R. C. Johnson, Phys. Rev. 177, 2472 (1969) ibid.182, 1755 (1969) ibid.185, 2020 (1969)
A. F. Antippa and A. E. Everett, Phys. Rev. 186, 1571 (1969) Phys. Rev. D 1, 606 (1970)
L. A. P. Balázs, Phys. Rev. 137, B1510 (1965)
N. Barash-Schmidt et al., Phys. Letters 33B, 1 (1970)
W. D. Walker, J. Carroll, A. Garfinkel, and B. Oh, Phys. Rev. Letters 18, 630 (1967) J. P. Baton, G. Laurens, and J. Reignier, Nucl. Phys. B3, 349 (1967)
J. H. Scharenguivel et al., Phys. Rev. 186, 1397 (1969)
E. Malamud and P. Schlein, Phys. Rev. Letters 19, 1056 (1967)
N. Khuri, Phys. Rev. 153, 1477 (1967)
J. Finkelstein, Phys. Rev. 145, 1185 (1966)

[c1] D. Morgan and G. Shaw, Phys. Rev. D 2, 520 (1970)

[c2] S. Weinberg, Phys. Rev. Letters 17, 616 (1966)

[c3] A. E. Everett, Phys. Rev. 173, 1663 (1968)

[c4] P. D. P. Collins and R. C. Johnson, Phys. Rev. 177, 2472 (1969) ibid.182, 1755 (1969) ibid.185, 2020 (1969)

[c5] A. F. Antippa and A. E. Everett, Phys. Rev. 186, 1571 (1969) Phys. Rev. D 1, 606 (1970)

[c6] L. A. P. Balázs, Phys. Rev. 137, B1510 (1965)

[c7] N. Barash-Schmidt et al., Phys. Letters 33B, 1 (1970)

[c8] W. D. Walker, J. Carroll, A. Garfinkel, and B. Oh, Phys. Rev. Letters 18, 630 (1967) J. P. Baton, G. Laurens, and J. Reignier, Nucl. Phys. B3, 349 (1967)

[c9] J. H. Scharenguivel et al., Phys. Rev. 186, 1397 (1969)

[c10] E. Malamud and P. Schlein, Phys. Rev. Letters 19, 1056 (1967)

[c11] N. Khuri, Phys. Rev. 153, 1477 (1967)

[c12] J. Finkelstein, Phys. Rev. 145, 1185 (1966)

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$S$ -Wave $π π$ Scattering in the Effective-Potential Approximation

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S-Wave ππ Scattering in the Effective-Potential Approximation

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References (12)

$S$ -Wave $π π$ Scattering in the Effective-Potential Approximation