High-Energy Bounds from Low-Energy Data

Richard Blankenbecler; Robert Savit

doi:10.1103/PhysRevD.5.2757

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High-Energy Bounds from Low-Energy Data

Richard Blankenbecler and Robert Savit

Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305

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Phys. Rev. D 5, 2757 – Published 1 June, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.2757

Abstract

A method for deriving rigorous upper bounds on asymptotic values of total cross sections is discussed. The size of the bound is determined by low-energy data. A functional form for the total cross section at high energies is assumed and bounds on the parameters introduced are obtained. The method is applied to $π - π$ scattering, and numerical estimates, using experimental data, are given for different parametrizations. For an asymptotically constant $σ_{T} (s)$ , we find $σ_{T} (\infty) ≲ 40$ mb. Better data would improve the accuracy of this bound and could lower it significantly.

References (5)

Omitted endnote
M. B. Einhorn and R. Blankenbecler, Ann. Phys. (N.Y.) 67, 480 (1971)
C. Schmid, CERN Report No. CERN-TH-1403 (unpublished) Proceedings of a Conference on ππ and Kπ Interactions, at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969) P. Baillon et al., SLAC Report No. SLAC-PUB-1016 (unpublished)
S. Krinsky, Phys. Rev. D 4, 1096 (1971)
L. Łukasuk and A. Martin, Cavendish Laboratory, Cambridge Univ. report, 1967 (unpublished)

[c1] Omitted endnote

[c2] M. B. Einhorn and R. Blankenbecler, Ann. Phys. (N.Y.) 67, 480 (1971)

[c3] C. Schmid, CERN Report No. CERN-TH-1403 (unpublished) Proceedings of a Conference on ππ and Kπ Interactions, at Argonne National Laboratory, 1969, edited by F. Loeffler and E. Malamud (Argonne National Laboratory, Argonne, Ill., 1969) P. Baillon et al., SLAC Report No. SLAC-PUB-1016 (unpublished)

[c4] S. Krinsky, Phys. Rev. D 4, 1096 (1971)

[c5] L. Łukasuk and A. Martin, Cavendish Laboratory, Cambridge Univ. report, 1967 (unpublished)

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High-Energy Bounds from Low-Energy Data

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