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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
"Analytic Extrapolations Techniques and Stability Problems in dispersion Theory". S. Ciulli, C. Pomponiu and I. Sabba-Stefanescu, Phys. Rep. 17 (1975) 133.
"Low and intermediate Energy Kaon-Nucleon Physics". E. Ferrari and G.Violini. Proceedings of the Workshop at the Institute of Physics of the University of Rome, March 1980. (D.Reidel P.Co.1980)
"Dispersion Theory in high energy physics". N.M. Queen and G. Violini. MacMillan Press Limited 1974.
"Magnitude of the σ-Term, Chiral Symmetry and Scale Invariance". G. Altarelli et al.. Phys. Lett. B 35 (1971) 415.
"Compilation of Coupling Constants and Low-Energy Parameters". N.M. Nagels et al. Nucl. Phys. B 147 (1979) 189.
"Phenomenological Dispersion Theory of KN Scattering". N.M. Queen, M. Restionoli and G. Violini, Fortschr. Phys. 21 (1973) 569.
"Summation of Series and Conformal Mapping". T.H. Gronwall, Annals of Math. (2), 33 (1932) 101.
"Approximants de Padé" J. Gilewicz. Lecture Notes in Mathematics 667 (1978).
"Padé type approximation and General Orthogonal Polynomials". C. Brezinski. Birkhauser Verlag ISNM 50 1980.
"Essentials of Padé Approximants". G.A. Baker. Academic Press 1975.
"Moment-theory Approximations for Non-negative Spectral Densities". C.T. Corcoran and P.W. Langhoff, J. Math. Phys. 18 (1977) 651.
"The problem of moments". J.A. Shoat and J.D. Tamarkin. American Mathematical Society. Mathematical Surveys I (1943).
"An introduction to orthogonal polynomials". T.S. Chihara, Gordon and Breack 1978.
"Dispersion Relations Constraints on Low Energy KN Scattering". A.D. Martin, Phys. Lett. 65 B (1976) 346.
"Compilation of K± Cross Sections." CERN-HERA 79-02 (1979).
"Phenomenology of Total Cross Sections and Forward Scattering at High Energy". V. Barger and R.J.N. Phillips, Nucl. Phys. B 32 (1971) 93.
"Compilation of Real Parts of the K±p Forward Elastic Amplitude, Report UB-Kp-1-78 (1978). Birmingham.
"K±p Elastic Scattering from 130 to 755 Nev/c". W. Cameron et al. Nucl. Phys. B 78 (1974) 93.
"The Zero-Energy Kp Scattering Amplitude and the Evaluation of the Kaon-Nucleon Sigma-Terms". A.D. Martin and G. Violini. Lett. Nuovo Cim. 30 (1981) 105.
"On Determinations of the KN Effective Coupling Constant from Forward Amplitudes". N. Sznalder-Hald et al., Nucl. Phys. B 59 (1973) 93.
"A Use of Zeros in Evaluating the K±p Forward Scattering Amplitudes". G.K. Atkin, J.E. Bowcock and N.M. Queen, J. Phys. G: Nucl. Phys. 7 (1981) 613.
"Dispersion Analysis of the K±p Forward Scattering Amplitudes" B. di Claudio, G. Violini and N.M. Queen, Nucl. Phys. B 161 (1979) 238.
"Positivity as a Constraint on the Positions of the Zeros of the K−p Forward Scattering Amplitude". G.K. Atkin, J.E. Bowcock and N.M. Queen, Z. Phys. C 15 (1982) 129.
"Kaon Nucleon Parameters". A.D. Martin. Nucl. Phys. B 179(1981) 33.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0072469
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17212-3
Online ISBN: 978-3-540-47412-8
eBook Packages: Springer Book Archive
