Few-Body Systems

, 59:96 | Cite as

From Experimental Data to Pole Parameters in a Direct Way (Angle Dependent Continuum Ambiguity and Laurent + Pietarinen Expansion)

  • A. ŠvarcEmail author
  • Y. Wunderlich
  • H. Osmanović
  • M. Hadžimehmedović
  • R. Omerović
  • J. Stahov
  • V. Kashevarov
  • K. Nikonov
  • M. Ostrick
  • L. Tiator
  • R. Workman
Part of the following topical collections:
  1. NSTAR 2017


Unconstrained partial-wave amplitudes obtained at discrete energies from fits to complete sets of eight independent observables which are required to uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and are in principle non-unique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photoproduction and show that the non-uniqueness effect can be removed through a phase rotation generating “up-to-a-phase” unique set of SE partial wave amplitudes. Extracting pole positions from partial wave amplitudes is the next step. Up to now, there was no reliable way to extract pole parameters from SE partial waves, but a new and simple single-channel method (Laurent + Pietarinen expansion) applicable for continuous and discrete data has been recently developed. It is based on applying the Laurent decomposition of partial wave amplitude, and expanding the non-resonant background into a power series of a conformal-mapping, quickly converging power series obtaining the simplest analytic function with well-defined partial wave analytic properties which fits the input. The generalization of this method to multi- channel case is also developed and presented. Unifying both methods in succession, one constructs a model independent procedure to extract pole parameters directly from experimental data without referring to any theoretical model.


  1. 1.
    A.D. Martin, T.D. Spearman, Elementary Particle Theory (North-Holland Publishing Company, Amsterdam, 1970)Google Scholar
  2. 2.
    D. Atkinson, P.W. Johnson, R.L. Warnock, Commun. Math. Phys. 33, 221 (1973)ADSCrossRefGoogle Scholar
  3. 3.
    J.E. Bowcock, H. Burkhard, Rep. Prog. Phys. 38, 1099 (1975)ADSCrossRefGoogle Scholar
  4. 4.
    D. Atkinson, I.S. Stefanescu, Commun. Math. Phys. 101, 291 (1985)ADSCrossRefGoogle Scholar
  5. 5.
    A.V. Anisovich, R. Beck, E. Klempt, V.A. Nikonov, A.V. Sarantsev, U. Thoma, Eur. Phys. J. A 48, 15 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    L. Tiator, D. Drechsel, S.S. Kamalov, M. Vanderhaeghen, Eur. Phys. J. ST 198, 141 (2011)CrossRefGoogle Scholar
  7. 7.
    A.M. Sandorfi, S. Hoblit, H. Kamano, T.-S.H. Lee, J. Phys. G: Nucl. Part. Phys. 38, 053001 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    A.S. Omalaenko, Sov. J. Nucl. Phys. 34(3), 406–411 (1981)Google Scholar
  9. 9.
    N.W. Dean, P. Lee, Phys. Rev. D 5, 2741 (1972)ADSCrossRefGoogle Scholar
  10. 10.
    G. Keaton, R. Workman, Phys. Rev. C 54, 1437 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, L. Tiator, R.L. Workman, Phys. Rev. C88, 035206 (2013)ADSGoogle Scholar
  12. 12.
    A. Svarc, M. Hadzimehmedovic, R. Omerovic, H. Osmanovic, J. Stahov. Phys. Rev. C89, 0452205 (2014)Google Scholar
  13. 13.
    A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, L. Tiator, R.L. Workman, Phys. Rev. C89, 65208 (2014)ADSGoogle Scholar
  14. 14.
    J. Dougall, Glasg. Math. J. 1, 121–125 (1952)MathSciNetGoogle Scholar
  15. 15.
    Y. Wunderlich, A. Švarc, R.L. Workman, L. Tiator, R. Beck, Phys. Rev. C 96, 065202 (2017)ADSCrossRefGoogle Scholar
  16. 16.
    see R.L. Workman, M.W. Paris, W.J. Briscoe, L. Tiator, S. Schumann, M. Ostrick, S.S. Kamalov, EPJA (2011) 47:143, and references thereinGoogle Scholar
  17. 17.
    V.L. Kashevarov, L. Tiator, M. Ostrick, Bled Workshops Phys. 16, 9 (2015)Google Scholar
  18. 18.
    V. L. Kashevarov, l. Tiator, M. Ostrick, JPS Conf. Proc. 13, 020029 (2017)Google Scholar
  19. 19.
  20. 20.
    R.L. Workman, L. Tiator, Y. Wunderlich, M. Doering, H. Haberzettl, Phys. Rev. C 95, 015206 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    J. Nys, V. Mathieu, C. Fernndez-Ramrez, A.N. Hiller Blin, A. Jackura, M. Mikhasenko, A. Pilloni, A.P. Szczepaniak, G. Fox, J. Ryckebusch, Phys. Rev. D 95, 034014 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    R.L. Workman, M.W. Paris, W.J. Briscoe, L. Tiator, S. Schumann, M. Ostrick, S.S. Kamalov, Eur. Phys. J. A 47, 143 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    S. Ciulli, J. Fischer, Nucl. Phys. 24, 465 (1961)Google Scholar
  24. 24.
    I. Ciulli, S. Ciulli, J. Fisher, Nuovo Cimento 23, 1129 (1962)CrossRefGoogle Scholar
  25. 25.
    E. Pietarinen, Nuovo Cimento Soc. Ital. Fis. 12A, 522 (1972)ADSCrossRefGoogle Scholar
  26. 26.
    E. Pietarinen, Nucl. Phys. B 107, 21 (1976)ADSCrossRefGoogle Scholar
  27. 27.
    Michiel Hazewinkel: Encyclopaedia of Mathematics, Vol. 6, Springer, 31. 8. p. 251 (1990)Google Scholar
  28. 28.
    G. Höhler, H. Schopper, Numerical data and functional relationships in science and technology. Group I: Nuclear and particle physics. Vol. 9: Elastic and charge exchange scattering of elementary particles. B: Pion Nucleon Scattering. Pt. 2: Methods and results and phenomenology. Springer, Berlin ( 1983). ( Landolt-Boernstein. New Series, I/9B2)Google Scholar
  29. 29.
    A. Švarc, M. Hadžimehmedović, H. Osmanović, J. Stahov, L. Tiator, R.L. Workman, Phys. Lett. B755, 452–455 (2016)ADSGoogle Scholar
  30. 30.
    A. Švarc, M. Hadžimehmedović, H. Osmanović, J. Stahov, R.L. Workman, Phys. Rev. C91, 015207 (2015)ADSGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Rudjer Bošković InstituteZagrebCroatia
  2. 2.Helmholtz-Institut für Strahlen- und Kernphysik der Universitöt BonnBonnGermany
  3. 3.Faculty of Natural Sciences and MathematicsUniversity of TuzlaTuzlaBosnia and Herzegovina
  4. 4.Institut für KernphysikUniversität MainzMainzGermany
  5. 5.Data Analysis Center at the Institute for Nuclear Studies, Department of PhysicsThe George Washington UniversityWashingtonUSA

Personalised recommendations