Frontiers of Physics

, 14:24501 | Cite as

On the existence of N*(890) resonance in S11 channel of πN scatterings

  • Yu-Fei Wang
  • De-Liang YaoEmail author
  • Han-Qing Zheng


Low-energy partial-wave πN scattering data is reexamined with the help of the production representation of partial-wave S matrix, where branch cuts and poles are thoroughly under consideration. The left-hand cut contribution to the phase shift is determined, with controlled systematic error estimates, by using the results of O(p3) chiral perturbative amplitudes obtained in the extended-onmass- shell scheme. In S11 and P11 channels, severe discrepancies are observed between the phase shift data and the sum of all known contributions. Statistically satisfactory fits to the data can only be achieved by adding extra poles in the two channels. We find that a S11 resonance pole locates at \(\sqrt {{z_r}} \) = (0:895–0:081)–(0:164–0:023)i GeV, on the complex s-plane. On the other hand, a P11 virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at \(\sqrt {{z_v}} \) = (0:966–0:018) GeV, slightly above the nucleon pole on the real axis below threshold. Physical origin of the two newly established poles is explored to the best of our knowledge. It is emphasized that the O(p3) calculation greatly improves the fit quality comparing with the previous O(p2) one.


dispersion relations πN scatterings nucleon resonance 



One of the authors (YFW) acknowledges Helmholtz-Institut für Strahlen- und Kernphysik of Bonn University, for warm hospitality where part of this work is being done; and thanks Bastian Kubis and Ulf-G. Meißner for helpful discussions. This work was supported in part by the National Natural Science Foundations of China (NSFC) under Contract Nos. 10925522 and 11021092; the Spanish Ministerio de Economía y Competitividad (MINECO) and the European Regional Development Fund (ERDF), under contracts FIS2014-51948-C2-1-P, FIS2014-51948- C2-2-P, FIS2017-84038-C2-1-P, FIS2017-84038-C2-2-P, and SEV- 2014-0398; and the Generalitat Valenciana under contract PROMETEOII/2014/0068.


  1. 1.
    G. F. Chew, M. L. Goldberger, F. E. Low, and Y. Nambu, Application of dispersion relations to low-energy mesonnucleon scattering, Phys. Rev. 106(6), 1337 (1957)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. A. Logunov, L. D. Soloviev, and A. N. Tavkhelidze, Dispersion sum rules and high-energy scattering, Phys. Lett. B 24(4), 181 (1967)ADSCrossRefGoogle Scholar
  3. 3.
    K. Igi and S. Matsuda, New sum rules and singularities in the complex J plane, Phys. Rev. Lett. 18(15), 625 (1967)ADSCrossRefGoogle Scholar
  4. 4.
    R. Dolen, D. Horn, and C. Schmid, Finite energy sum rules and their application to πN charge exchange, Phys. Rev. 166(5), 1768 (1968)ADSCrossRefGoogle Scholar
  5. 5.
    G. Höhler, Pion-Nucleon Scattering, Landolt-Börnstein, Vol. 962, edited by H. Schopper, Berlin: Springer, 1983Google Scholar
  6. 6.
    R. Koch and E. Pietarinen, Low-energy πN partial wave analysis, Nucl. Phys. A 336(3), 331 (1980)ADSCrossRefGoogle Scholar
  7. 7.
    R. Koch, A calculation of low-energy πN partial waves based on fixed t analyticity, Nucl. Phys. A 448(4), 707 (1986)ADSCrossRefGoogle Scholar
  8. 8.
    E. Matsinos, W. S. Woolcock, G. C. Oades, G. Rasche, and A. Gashi, Phase-shift analysis of low-energy π ± p elastic-scattering data, Nucl. Phys. A 778(1–2), 95 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    R. A. Arndt, W. J. Briscoe, I. I. Strakovsky, and R. L. Workman, Extended partial-wave analysis of πN scattering data, Phys. Rev. C 74(4), 045205 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    E. E. Jenkins and A. V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255(4), 558 (1991)ADSCrossRefGoogle Scholar
  11. 11.
    V. Bernard, N. Kaiser, and U. G. Meiβner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 4(02), 193 (1995)ADSCrossRefGoogle Scholar
  12. 12.
    V. Bernard, Chiral perturbation theory and baryon properties, Prog. Part. Nucl. Phys. 60(1), 82 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    J. Gasser, M. E. Sainio, and A. Svarc, Nucleons with chiral loops, Nucl. Phys. B 307(4), 779 (1988)ADSCrossRefGoogle Scholar
  14. 14.
    T. Fuchs, J. Gegelia, G. Japaridze, and S. Scherer, Renormalization of relativistic baryon chiral perturbation theory and power counting, Phys. Rev. D 68(5), 056005 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    J. M. Alarcon, J. Martin Camalich, and J. A. Oller, Improved description of the πN-scattering phenomenology in covariant baryon chiral perturbation theory, Ann. Phys. 336, 413 (2013)ADSCrossRefGoogle Scholar
  16. 16.
    Y. H. Chen, D. L. Yao, and H. Q. Zheng, Analyses of pion-nucleon elastic scattering amplitudes up to O(p 4) in extended-on-mass-shell subtraction scheme, Phys. Rev. D 87(5), 054019 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    D.-L. Yao, D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, J. Gegelia, H. Krebs, and U.-G. Meiβner, Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances, J. High Energy Phys. 2016, 38 (2016)CrossRefGoogle Scholar
  18. 18.
    D. Siemens, V. Bernard, E. Epelbaum, A. Gasparyan, H. Krebs, and U. G. Meiβner, Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look, Phys. Rev. C 94(1), 014620 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, H. Krebs, and U. G. Meiβner, Elastic and inelastic pionnucleon scattering to fourth order in chiral perturbation theory, Phys. Rev. C 96(5), 055205 (2017)CrossRefGoogle Scholar
  20. 20.
    M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U. G. Meiβner, Roy–Steiner-equation analysis of pion-nucleon scattering, Phys. Rep. 625, 1 (2016)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    A. Gasparyan and M. F. M. Lutz, Photon-and pionnucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian, Nucl. Phys. A 848(1–2), 126 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    V. Mathieu, I. V. Danilkin, C. Fernndez-Ramrez, M. R. Pennington, D. Schott, A. P. Szczepaniak, and G. Fox, Toward complete pion nucleon amplitudes, Phys. Rev. D 92(7), 074004 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    Y. F. Wang, D. L. Yao, and H. Q. Zheng, New insights on low energy πN scattering amplitudes, Eur. Phys. J. C 78(7), 543 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    Z. Xiao and H. Q. Zheng, Left-hand singularities, hadron form-factors and the properties of the sigma meson, Nucl. Phys. A 695(1–4), 273 (2001)ADSGoogle Scholar
  25. 25.
    H. Q. Zheng, Z. Y. Zhou, G. Y. Qin, Z. Xiao, J. J. Wang, and N. Wu, The kappa resonance in s wave πK scatterings, Nucl. Phys. A 733(3–4), 235 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    Z. Y. Zhou and H. Q. Zheng, An improved study of the kappa resonance and the non-exotic s wave πK scatterings up to xxxx = 2.1 GeV of LASS data, Nucl. Phys. A 775(3–4), 212 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    Z. Y. Zhou, G. Y. Qin, P. Zhang, Z. Xiao, H. Q. Zheng, and N. Wu, The Pole structure of the unitary, crossing symmetric low energy pp scattering amplitudes, J. High Energy Phys. 02, 043 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. 96(13), 132001 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    S. Descotes-Genon and B. Moussallam, The K*0 (800) scalar resonance from Roy-Steiner representations of πK scattering, Eur. Phys. J. C 48(2), 553 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    Z. H. Guo, J. J. Sanz-Cillero, and H. Q. Zheng, Partial waves and large N C resonance sum rules, J. High Energy Phys. 06, 030 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Z. H. Guo, J. J. Sanz-Cillero, and H. Q. Zheng, O(p 6) extension of the large-N C partial wave dispersion relations, Phys. Lett. B 661, 342 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Partial wave analysis of all nucleonnucleon scattering data below 350-MeV, Phys. Rev. C 48(2), 792 (1993)ADSCrossRefGoogle Scholar
  33. 33.
    D. R. Entem and J. A. Oller, The N/D method with non-perturbative left-hand-cut discontinuity and the 1S0 NN partial wave, Phys. Lett. B 773, 498 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    Y. F. Wang, D. L. Yao, and H. Q. Zheng, New insights on low energy πN scattering amplitudes II: Comprehensive analyses at O(p 3) level, arXiv: 1811.09748 (2018)Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  2. 2.Instituto de Física Corpuscular (centro mixto CSIC-UV)Institutos de Investigación de PaternaApartado, ValenciaSpain
  3. 3.Collaborative Innovation Center of Quantum MatterBeijingChina

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