How does the S ₁₁ N*(890) state emerge from a naive K-matrix fit?

Abstract

We give a pedagogical analysis on K-matrix models describing the πN 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.

A dispersive analysis of low energy pion photo- and electroproduction

“…[33]). Further, some follow-up work confirmed this discovery in different ways such as 𝐾matrix [34] and 𝑁/𝐷 method [35]. It could be surprising to notice that the pole position, is located below the threshold 𝑠 𝑅 .…”

An $N/D$ study of the $S_{11}$ channel $πN$ scattering amplitude

“…The N/D calculations discussed in this paper are of rather complicated dynamical ones, however the production representation has been shown to be useful in providing us a simple and pictorial way of understanding the essence of the N/D calculations: the evidence of the existence of N * (890) seems to be at least partly from the peculiar singularity structure of the background integral defined in Eqs. (9). It reads that if T (s = 0) does not vanish (or does not vanish fast enough), then an s-wave subthreshold resonance exist, in the most attractive channels.…”

“…The result is obtained by using the production representation (PKU representation) for partial wave amplitudes [4] [5] [6] [7] [8]. It is found later that the N * (890) pole may also be generated from a conventional and simple K-matrix fit, though the latter suffers from the existence of spurious poles on 1st Riemann sheet of complex s plane [9]. Properties of N * (890) are also investigated, such as its coupling to N γ and N π [10], and N γ * [11].…”

On Lowest Lying $\frac{1}{2}^-$ Octet Baryons

“…[9] for a review). Later the existence of N * (890) is also confirmed by a K-matrix analysis, [10] and the N/D studies. [11,12] Since the existence of N * (890) does not seem to be well accepted yet in the physics community, further evidences need to be gathered, which may be done by making the study in flavor SU (3) basis, by associating N * (890) with (sub-threshold) resonances investigated in other channels -which is the main purpose of this note.…”