New insights on low energy πN scattering amplitudes:comprehensive analyses at ■(p^3) level

A production representation of partial-wave S matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the ■(p^3) results obtained in covariant baryon chiral perturbation theory within the extendedon-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in S11 and P11 channels, as conjectured in our previous paper [Eur. Phys. J. C, 78(7): 543(2018)], are firmly established. Specifically, the pole mass of the S11 hidden resonance is determined to be(895±81)-(164±23)i MeV,whereas,the virtual pole in the P11 channel locates at(966±18) MeV. It is found that analyses at the■(p^3) level improves significantly the fit quality, comparing with the previous■(p^2) one. Quantitative studies with cautious physical discussions are also conducted for the other S-and P-wave channels.

On the existence of N^*(890) resonance in Sn 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(p^3) chiral perturbative amplitudes obtained in the extended-onmass- shell scheme. In Sn and Pu 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 Sn resonance pole locates at √zr=(0.895 ±0.081)—(0.164±0.023)i GeV, on the complex s-plane. On the other hand, a Fn virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at √zv=(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 oiir knowledge. It is emphasized that the O(p^3) calculation greatly improves the fit quality comparing with the previous O(p^2) one.

How does the S11 N^*(890) state emerge from a naive K-matrix fit?

We give a pedagogical analysis on K-matrix models describing theπN scattering amplitude,in S11 channel at low energies.We show how the correct use of analyticity in the s-channel and crossing symmetry in t-and u-channels leads to a much improved analytic behavior in the negative s region,in agreement with the prediction from chiral perturbation amplitudes in its validity region.The analysis leads again to the conclusion that a genuine N^*(890)resonance exists.

Singularities and accumulation of singularities ofπN scattering amplitudes

It is demonstrated that for the isospin I=1/2πN scattering amplitude,T^(I=1/2)(s,t),s=(m_(N)^(2)-m_(π)^(2))^(2)/m_(N)^(2)and s=m_(N)^(2)+2m_(π)^(2)are two accumulation points of poles on the second sheet of complex s plane,and are hence accumulation of singularities of T^(I=1/2)(s,t).For T^(I=3/2)(s,t),s=(m_(N)^(2)-m_(π)^(2))^(2)/m_(N)^(2)is the accumulation point of poles on the second sheet of the complex s plane.The proof is valid up to all orders of chiral expansions.

Production representation of partial wave scattering amplitudes and the fo（600） particle

The establishlnent of production representation of partial wave scattering alnplitudes is reviewed in the context of quantum field theory. Its relation to the production representation, or Ning Hu representation in quantum mechanical scattering theory is pointed out. One of the most important application of the production representation is the physics of the fo（600） and K（700） scalar hadron resonances, on which we also give a brief review. It is emphasized that all evidences accunmlated so far are consistent with the picture that the fo（600） meson is the chiral partner of the Nambu Goldstone bosons in a linear realization of chiral symmetry.