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(p 3 ) chiral perturbative amplitudes obtained in the extended-on-mass-shell scheme. In S 11 and P 11 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 S 11 resonance pole locates at √ z r = (0.895 ± 0.081) − (0.164 ± 0.023)i GeV, on the complex s-plane. On the other hand, a P 11 virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at √ 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(p 3 ) calculation greatly improves the fit quality comparing with the previous O(p 2 ) one.The studies in the field of πN scatterings have led to and fertilized many useful ideas and methods in the development of hadron and even particle physics, such as the establishment of dispersion techniques [1], the concepts of finite energy sum rules [2, 3] and duality [4]. In decades, a wealth of experimental data on differential cross section and polarizations [5] has been accumulated. Partial wave analysis of the πN scattering amplitudes has also been performed which results in the discovery of many baryon resonances [6][7][8][9].Efforts in modern studies on πN scatterings focus on a precision description of the πN amplitudes, not only in the physical region but also in the subthreshold region. Baryon chiral perturbation theory (BChPT) [10-12] serves as an appropriate tool for such a purpose, at low energies. The problem of power counting breaking terms [13] in loops, caused by the presence of baryon degrees of freedom in the chiral Lagrangian, is finally overcome by the use of the extended-on-mass-shell subtraction scheme [14]. Though many achievements have been obtained in the perturbation calculations within this scheme [15][16][17][18][19], analyses respecting both exact partial wave unitarity and proper analyticity are still lacking. Hence the use of the dispersion techniques revived in recent years. For example, the analysis based on Roy-Steiner equations [20] has reproduced low-energy phase shift data successfully (see also Refs. [21,22]).More recently, in Ref.[23], low-energy πN scattering has been re-visited with the help of the Peking University (PKU) representation [24-27] -a production parametrization of the unitary partial wave S matrix for two-body elastic scattering amplitudes. The production representation is constructed from first principles. Especially, analyticity and unitarity are automatically built in, hence the fatal defic...

An N/D study of the S 11 channel πN scattering amplitude *

“…In our study of N scatterings, however, an unexpected new phenomenon occurs. Essentially, the cut structure of the background phase shift, , must be modified, due to the presence of the -channel nucleon exchange 1) . As a result, an additional contribution exists in the expression of , which is approximately canceled by the contributions from the two newly found virtual poles, located near the end points (i.e., and defined in Fig.…”

“…numerically smaller than the cut lying on (previous examples can be found in Refs. [1,4,9]). Hence, a large and positive at is important, as suggested in Fig.…”

“…The PT outputs may be selected as an input here, as is adopted in Refs. [1][2][3]. A careful analysis reveals, however, that the partial wave pro- 023104-4 χ s = 0 jection of PT amplitudes encounters a rather severe problem at .…”

“…In recent literature [1][2][3], it has been suggested that there exists a sub-threshold nucleon resonance hidden in the channel of scatterings, with a pole mass GeV. The result was obtained by using the production representation (PKU representation) for partial wave amplitudes [4][5][6][7][8].…”

A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation

“…A subthreshold resonance: from πN scattering Recently, in Refs. [334,335,336], a novel subthreshold resonance named N * (890) was found in the S 11 wave of the πN interaction when applying the PKU representation [211,337,210,338,212,300] to analyze the covariant chiral amplitude of elastic πN scattering [95,96,100,101] at low energies.…”