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A Stieltjes analysis of the K+-p forward elastic amplitude

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1237)

Abstract

The positivity hypothesis on an unknown function X*(x), related to the imaginary part of the K+-p scattering amplitude on the unphysical region, allows the construction of a Stieltjes function H(z), known in a discrete set of real points and affected by errors owing to experimental measurements.

The Stieltjes character of H(z) imposes constraints on the coefficients of its formal expansion which limit the universe of approximant functions, so acting as stabilizers of the analytic extrapolation.

The Pade approximants (P.A.) to H(z), built with the coefficients of the formal expansion, provide rigorous bounds on the function in the cut complex plane.

These bounds on H(z) can be translated to the K+- amplitude, F±(ω), obtaining bounds on the coupling constants g 2KNΛ and g 2KNΣ .

Taking advantage of the fact that P.A. are valid for complex values of z, the position of the complex conjugate zeros of the amplitude has also been calculated.

The consistency of the calculated real part has been successfully checked by taking different absorption points with the latter values of real parts.

The stability of the method of extrapolation has been confirmed using a model function, whose analytical structure is perfectly known, perturbed randomly according to the experimental errors.

The addition of the hypothesis of unimodality of X*(x) provides tighter rigorous bounds on H(z) on the cut complex plane and the obtention of upper and lower moment sequences of X*(x) allowed by our two general hypotheses.

The inversion of these moment sequences using a Stieltjes-Tchebycheff technique allows the calculation of the scattering amplitude F±(ω) even on the unphysical cut, so achieving the rational parametrization of the amplitude in the whole ω complex plane.

Keywords

  • Moment Sequence
  • Pade Approximants
  • Elastic Amplitude
  • Hankel Determinant
  • Stieltjes Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1987 Springer-Verlag

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Antolin, J., Cruz, A. (1987). A Stieltjes analysis of the K+-p forward elastic amplitude. In: Gilewicz, J., Pindor, M., Siemaszko, W. (eds) Rational Approximation and its Applications in Mathematics and Physics. Lecture Notes in Mathematics, vol 1237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072469

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  • DOI: https://doi.org/10.1007/BFb0072469

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