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Dynamical Theory for Strong Interactions at Low Momentum Transfers but Arbitrary Energies

Chew, Geoffrey F. and Frautschi, Steven C. (1961) Dynamical Theory for Strong Interactions at Low Momentum Transfers but Arbitrary Energies. Physical Review, 123 (4). pp. 1478-1486. ISSN 0031-899X. doi:10.1103/PhysRev.123.1478.

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Starting from the Mandelstam representation, it is argued on physical grounds that "strips" along the boundaries of the double spectral regions are likely to control the physical elastic scattering amplitude for arbitrarily high energies at small momentum transfers. Pion-pion scattering is used as an illustration to show how the double spectral functions in the nearest strip regions may be calculated, and an attempt is made to formulate an approximate but "complete" set of dynamical equations. The asymptotic behavior of the solutions of these equations is discussed, and it is shown that if the total cross section is to approach a constant at large energies then at low energy the S-dominant ππ solution is inadmissible. A principle of "maximum strength" for strong interactions is proposed, and it is argued that such a principle will allow large low-energy phase shifts only for l<~lmax, where lmax~1.

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Additional Information:© 1961 The American Physical Society. Received 30 March 1961. We are deeply indebted to M. Froissart, M. Gell-Mann, and S. Mandelstam for criticism of the ideas presented here. We are also grateful for discussions with V. Singh and B.M. Udgaonkar, whose paper on the πN problem immediately follows, and to J.Charap, who has been studying potential scattering by the analogous approach. Research supported in part by the U.S. Atomic Energy Commission and in part by the National Science Foundation. Note added in proof. After completion of this manuscript we received a paper by K.A. Ter-Martirosyan, J. Exptl. Theoret. Phys. (U.S.S.R.) 39, 827 (1960) [translation: Soviet Phys. - JETP 12, 575 (1961)], in which the same equations obtained here are derived.
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Atomic Energy CommissionUNSPECIFIED
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Deposited On:14 Jun 2008
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