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


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.

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  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)

    ADS  MathSciNet  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  5. 5.

    G. Höhler, Pion-Nucleon Scattering, Landolt-Börnstein, Vol. 962, edited by H. Schopper, Berlin: Springer, 1983

  6. 6.

    R. Koch and E. Pietarinen, Low-energy πN partial wave analysis, Nucl. Phys. A 336(3), 331 (1980)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  12. 12.

    V. Bernard, Chiral perturbation theory and baryon properties, Prog. Part. Nucl. Phys. 60(1), 82 (2008)

    ADS  Article  Google Scholar 

  13. 13.

    J. Gasser, M. E. Sainio, and A. Svarc, Nucleons with chiral loops, Nucl. Phys. B 307(4), 779 (1988)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    Article  Google 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)

    ADS  Article  Google 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)

    Article  Google 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)

    ADS  MathSciNet  Article  Google 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. A848(1–2), 126 (2010)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  33. 33.

    D. R. Entem and J. A. Oller, The N/D method with non-perturbative left-hand-cut discontinuity and the 1S0NN partial wave, Phys. Lett. B 773, 498 (2017)

    ADS  Article  Google 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 

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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.

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Correspondence to De-Liang Yao.

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Wang, Y., Yao, D. & Zheng, H. On the existence of N*(890) resonance in S11 channel of πN scatterings. Front. Phys. 14, 24501 (2019). https://doi.org/10.1007/s11467-018-0877-9

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  • dispersion relations
  • πN scatterings
  • nucleon resonance