Elsevier

Nuclear Physics B

Volume 82, Issue 2, 25 November 1974, Pages 347-364
Nuclear Physics B

Determination of the real parts of the K±p forward scattering amplitudes and a reduced KNY coupling constant consistent with dispersion relations

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Abstract

A type of modified dispersion relation and an iterative procedure are introduced, which allow the self-consistent determination of the real parts of the forward K±p scattering amplitude. The free parameters, which are determined by a linear fit in which all available data enter on real and imaginary parts, are the real and imaginary parts of the amplitude in an arbitrary point of the complex energy plane. Particularly taking the point at one of the poles, the value of the residue and that of the derivative of the residue function at that point are calculated.

By this procedure, a correlation is found between a reduced coupling constant Ḡ = G2Λ + 0.6 G2Σ and the s-wave K+p and scattering lenght a1s, the relation Ḡ2 = −253a1s − 59.83 being obtained.

Using a version of the dispersion relation, a value a1s = 0.296 fm is determined, which yelds Ḡ2 = 15.12.

Simultaneously the real parts over a wide range of energies are determined.

We illustrate the independence of the calculations with respect to the parametrization used for the imaginary part of the amplitude in the unphysical region.

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    Present address: Universidad de Piura, Ap. 353, Piura, Peru.

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