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

Abstract

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.

Keywords

dispersion relations / πN scatterings / nucleon resonance

References

[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)

[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)

[3] K. Igi and S. Matsuda, New sum rules and singularities in the complex J plane, Phys. Rev. Lett. 18(15), 625 (1967)

[4] R. Dolen, D. Horn, and C. Schmid, Finite energy sum rules and their application to πNcharge exchange, Phys. Rev. 166(5), 1768 (1968)

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

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

[7] R. Koch, A calculation of low-energy πN partial waves based on fixed t analyticity, Nucl. Phys. A 448(4), 707 (1986)

[8] E. Matsinos, W. S. Woolcock, G. C. Oades, G. Rasche, and A. Gashi, Phase-shift analysis of low-energy π^±pelastic-scattering data, Nucl. Phys. A 778(1–2), 95 (2006)

[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)

[10] E. E. Jenkins and A. V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255(4), 558 (1991)

[11] V. Bernard, N. Kaiser, and U. G. Meißner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 4(02), 193 (1995)

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

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

[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)

[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)

[16] Y. H. Chen, D. L. Yao, and H. Q. Zheng, Analyses of pion-nucleon elastic scattering amplitudes up to O(p⁴) in extended-on-mass-shell subtraction scheme, Phys. Rev. D 87(5), 054019 (2013)

[17] D.-L. Yao, D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, J. Gegelia, H. Krebs, and U.-G. Meißner, Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances, J. High Energy Phys. 2016, 38 (2016)

[18] D. Siemens, V. Bernard, E. Epelbaum, A. Gasparyan, H. Krebs, and U. G. Meißner, Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look, Phys. Rev. C 94(1), 014620 (2016)

[19] D. Siemens, V. Bernard, E. Epelbaum, A. M. Gasparyan, H. Krebs, and U. G. Meißner, Elastic and inelastic pionnucleon scattering to fourth order in chiral perturbation theory, Phys. Rev. C 96(5), 055205 (2017)

[20] M. Hoferichter, J. Ruiz de Elvira, B. Kubis, and U. G. Meißner, Roy–Steiner-equation analysis of pion-nucleon scattering, Phys. Rep. 625, 1 (2016)

[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)

[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)

[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)

[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)

[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)

[26] Z. Y. Zhou and H. Q. Zheng, An improved study of the kappa resonance and the non-exotic s wave πKscatterings up to s= 2.1 GeV of LASS data, Nucl. Phys. A 775(3–4), 212 (2006)

[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)

[28] I. Caprini, G. Colangelo, and H. Leutwyler, Mass and width of the lowest resonance in QCD, Phys. Rev. Lett. 96(13), 132001 (2006)

[29] S. Descotes-Genon and B. Moussallam, The K*0 (800) scalar resonance from Roy-Steiner representations of πKscattering, Eur. Phys. J. C 48(2), 553 (2006)

[30] Z. H. Guo, J. J. Sanz Cillero, and H. Q. Zheng, Partial waves and large N_Cresonance sum rules, J. High Energy Phys. 06, 030 (2007)

[31] Z. H. Guo, J. J. Sanz-Cillero, and H. Q. Zheng, O(p⁶) extension of the large-N_C partial wave dispersion relations, Phys. Lett. B 661, 342 (2008)

[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)

[33] D. R. Entem and J. A. Oller, The N/D method with non-perturbative left-hand-cut discontinuity and the ¹S₀NNpartial wave, Phys. Lett. B 773, 498 (2017)

[34] Y. F. Wang, D. L. Yao, and H. Q. Zheng, New insights on low energy πNscattering amplitudes II: Comprehensive analyses at O(p³) level, arXiv: 1811.09748 (2018)

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