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

Abstract

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.

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References

  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)

    ADS  Article  Google Scholar 

  3. 3.

    J.E. Bowcock, H. Burkhard, Rep. Prog. Phys. 38, 1099 (1975)

    ADS  Article  Google Scholar 

  4. 4.

    D. Atkinson, I.S. Stefanescu, Commun. Math. Phys. 101, 291 (1985)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  6. 6.

    L. Tiator, D. Drechsel, S.S. Kamalov, M. Vanderhaeghen, Eur. Phys. J. ST 198, 141 (2011)

    Article  Google Scholar 

  7. 7.

    A.M. Sandorfi, S. Hoblit, H. Kamano, T.-S.H. Lee, J. Phys. G: Nucl. Part. Phys. 38, 053001 (2011)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  10. 10.

    G. Keaton, R. Workman, Phys. Rev. C 54, 1437 (1996)

    ADS  Article  Google Scholar 

  11. 11.

    A. Svarc, M. Hadzimehmedovic, H. Osmanovic, J. Stahov, L. Tiator, R.L. Workman, Phys. Rev. C88, 035206 (2013)

    ADS  Google 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)

    ADS  Google Scholar 

  14. 14.

    J. Dougall, Glasg. Math. J. 1, 121–125 (1952)

    MathSciNet  Google Scholar 

  15. 15.

    Y. Wunderlich, A. Švarc, R.L. Workman, L. Tiator, R. Beck, Phys. Rev. C 96, 065202 (2017)

    ADS  Article  Google 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 therein

  17. 17.

    V.L. Kashevarov, L. Tiator, M. Ostrick, Bled Workshops Phys. 16, 9 (2015)

  18. 18.

    V. L. Kashevarov, l. Tiator, M. Ostrick, JPS Conf. Proc. 13, 020029 (2017)

  19. 19.

    http://pwa.hiskp.uni-bonn.de/

  20. 20.

    R.L. Workman, L. Tiator, Y. Wunderlich, M. Doering, H. Haberzettl, Phys. Rev. C 95, 015206 (2017)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  23. 23.

    S. Ciulli, J. Fischer, Nucl. Phys. 24, 465 (1961)

  24. 24.

    I. Ciulli, S. Ciulli, J. Fisher, Nuovo Cimento 23, 1129 (1962)

    Article  Google Scholar 

  25. 25.

    E. Pietarinen, Nuovo Cimento Soc. Ital. Fis. 12A, 522 (1972)

    ADS  Article  Google Scholar 

  26. 26.

    E. Pietarinen, Nucl. Phys. B 107, 21 (1976)

    ADS  Article  Google Scholar 

  27. 27.

    Michiel Hazewinkel: Encyclopaedia of Mathematics, Vol. 6, Springer, 31. 8. p. 251 (1990)

  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)

  29. 29.

    A. Švarc, M. Hadžimehmedović, H. Osmanović, J. Stahov, L. Tiator, R.L. Workman, Phys. Lett. B755, 452–455 (2016)

    ADS  Google Scholar 

  30. 30.

    A. Švarc, M. Hadžimehmedović, H. Osmanović, J. Stahov, R.L. Workman, Phys. Rev. C91, 015207 (2015)

    ADS  Google Scholar 

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Correspondence to A. Švarc.

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This article belongs to the Topical Collection “NSTAR 2017—The International Workshop on the Physics of Excited Nucleons”.

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Švarc, A., Wunderlich, Y., Osmanović, H. et al. From Experimental Data to Pole Parameters in a Direct Way (Angle Dependent Continuum Ambiguity and Laurent + Pietarinen Expansion). Few-Body Syst 59, 96 (2018). https://doi.org/10.1007/s00601-018-1410-y

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