Absorption Model Applied to <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mo>−</mo><mi>π</mi></math></span> Scattering

L. Chan; V. Hagopian; P. K. Williams

doi:10.1103/PhysRevD.2.583

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Absorption Model Applied to $π - π$ Scattering

L. Chan^* and V. Hagopian^†

P. K. Williams

The University of Pennsylvania, Philadelphia, Pennsylvania 19104
The Florida State University, Tallahassee, Florida 32306

The Florida State University, Tallahassee, Florida 32306

^*Present address: Physics Department, Georgia Institute of Technology.
^†Present address: Physics Department, The Florida State University.

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Phys. Rev. D 2, 583 – Published 1 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.583

Abstract

A study of the possibility of using an absorption model to obtain a unique $s$ -wave $I = 0$ $π π$ phase shift from the reaction $π^{-} p \to π^{-} π^{+} n$ was made. Applying the model to combined data from several latoratories, we obtained a set of reasonable (but twofold ambiguous) values for the isospin-zero $s$ -wave phase shift ${δ_{0}}^{0}$ , using the isotropic moment of the dipion decay distribution. Values for ${δ_{0}}^{0}$ deduced by using the $s - p$ wave interference term in the dipion decay cross section agreed well with previous (twofold ambiguous) results obtained by extrapolation procedures. Comparing the two sets of twofold ambiguous solutions for ${δ_{0}}^{0}$ , the lower or "down" branch was preferred marginally in the dipion mass region below the $ρ$ meson. No unique conclusion could be drawn in the higher-mass region. We emphasize the model dependence of these results, but we believe that similar studies with improved statistics for $- t > μ^{2}$ would yield similar results. Good data for $- t < μ^{2}$ are required to do definitive model-independent analyses.

References (9)

S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968) V. Hagopian, in Proceedings of the Conference on $π π$ and $K π$ Scattering, Argonne National Laboratory, 1969, p. 149 (unpublished) B. Reynolds et al., Phys. Rev. 184, 1424 (1969) J. Scharenguivel et al., Phys. Rev. Letters 24, 332 (1970)
J. Banton and G. Laurens, Phys. Rev. 176, 1574 (1968)
G. Chew and F. Low, Phys. Rev. 113, 1640 (1959)
G. Kane and M. Ross, Phys. Rev. 177, 2353 (1969) G. Kane, in Proceedings of the Conference on $π π$ and $K π$ Scattering, [1], p. 533
P. K. Williams, Phys. Rev. D 1, 1312 (1970) [4]
F. Selleri, Lectures in Theoretical Physics (University of Colorado Press, Boulder, Colo., 1964)
P. K. Williams, Phys. Rev. 181, 1963 (1969)
K. Gottfried and J. D. Jackson, Nuovo Cimento 34, 757 (1964)
P. Johnson et al. Phys. Rev. 163, 1497 (1967)

[c1] S. Marateck et al., Phys. Rev. Letters 21, 1613 (1968) V. Hagopian, in Proceedings of the Conference on $π π$ and $K π$ Scattering, Argonne National Laboratory, 1969, p. 149 (unpublished) B. Reynolds et al., Phys. Rev. 184, 1424 (1969) J. Scharenguivel et al., Phys. Rev. Letters 24, 332 (1970)

[c2] J. Banton and G. Laurens, Phys. Rev. 176, 1574 (1968)

[c3] G. Chew and F. Low, Phys. Rev. 113, 1640 (1959)

[c4] G. Kane and M. Ross, Phys. Rev. 177, 2353 (1969) G. Kane, in Proceedings of the Conference on $π π$ and $K π$ Scattering, [1], p. 533

[c5] P. K. Williams, Phys. Rev. D 1, 1312 (1970) [4]

[c6] F. Selleri, Lectures in Theoretical Physics (University of Colorado Press, Boulder, Colo., 1964)

[c7] P. K. Williams, Phys. Rev. 181, 1963 (1969)

[c8] K. Gottfried and J. D. Jackson, Nuovo Cimento 34, 757 (1964)

[c9] P. Johnson et al. Phys. Rev. 163, 1497 (1967)

Physical Review D

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Absorption Model Applied to $π - π$ Scattering

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Absorption Model Applied to π−π Scattering

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Absorption Model Applied to $π - π$ Scattering