On the existence of N*(890) resonance in S11 channel of πN scatterings
Yu-Fei Wang1, De-Liang Yao2(), Han-Qing Zheng1,3
1. Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China 2. Instituto de Física Corpuscular (centro mixto CSIC-UV), Institutos de Investigación de Paterna, Apartado 22085, 46071, Valencia, Spain 3. Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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 = (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 = (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.
. [J]. Frontiers of Physics, 2019, 14(2): 24501.
Yu-Fei Wang, De-Liang Yao, Han-Qing Zheng. On the existence of N*(890) resonance in S11 channel of πN scatterings. Front. Phys. , 2019, 14(2): 24501.
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) https://doi.org/10.1103/PhysRev.106.1337
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) https://doi.org/10.1016/0370-2693(67)90487-X
R. Dolen, D. Horn, and C. Schmid, Finite energy sum rules and their application to πNcharge exchange, Phys. Rev. 166(5), 1768 (1968) https://doi.org/10.1103/PhysRev.166.1768
5
G. Höhler, Pion-Nucleon Scattering, Landolt-Börnstein, Vol. 962, edited by H. Schopper, Berlin: Springer, 1983
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) https://doi.org/10.1016/j.nuclphysa.2006.07.040
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) https://doi.org/10.1103/PhysRevC.74.045205
10
E. E. Jenkins and A. V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255(4), 558 (1991) https://doi.org/10.1016/0370-2693(91)90266-S
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) https://doi.org/10.1103/PhysRevD.68.056005
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) https://doi.org/10.1016/j.aop.2013.06.001
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) https://doi.org/10.1103/PhysRevD.87.054019
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) https://doi.org/10.1007/JHEP05(2016)038
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) https://doi.org/10.1103/PhysRevC.94.014620
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) https://doi.org/10.1103/PhysRevC.96.055205
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) https://doi.org/10.1016/j.physrep.2016.02.002
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) https://doi.org/10.1103/PhysRevD.92.074004
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) https://doi.org/10.1016/S0375-9474(01)01100-9
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) https://doi.org/10.1016/j.nuclphysa.2003.12.021
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) https://doi.org/10.1016/j.nuclphysa.2006.06.170
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)
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) https://doi.org/10.1140/epjc/s10052-006-0036-2
30
Z. H. Guo, J. J. Sanz Cillero, and H. Q. Zheng, Partial waves and large NCresonance 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-NC partial wave dispersion relations, Phys. Lett. B 661, 342 (2008) https://doi.org/10.1016/j.physletb.2008.01.073
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) https://doi.org/10.1103/PhysRevC.48.792
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) https://doi.org/10.1016/j.physletb.2017.09.012
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)
