Origin of resonances in the chiral unitary approach

We study the origin of the resonances associated with pole singularities of the scattering amplitude in the chiral unitary approach. We propose a “natural renormalization” scheme using the low-energy interaction and the general principle of the scattering theory. We develop a method to distinguish dynamically generated resonances from genuine quark states [Castillejo-Dalitz-Dyson (CDD) poles]  using the natural renormalization scheme and phenomenological fitting. Analyzing physical meson-baryon scatterings, we find that the $\Lambda (1405)$ resonance is largely dominated by the meson-baryon molecule component. In contrast, the $N(1535)$ resonance requires a sizable CDD pole contribution, while the effect of the meson-baryon dynamics is also important.

Figure 1

Real part of the loop function $G(\sqrt{s})$ for the $\overline{K}N$ channel when $a=a_{\text{natural}}$ is adopted. The $s$-channel scattering region is defined as $\sqrt{s}>M_T$.

Figure 2

Masses of the target baryons $M_i$ and threshold energies $M_i+m_i$ of channel $i$ for $S=-1$ and $I=0$ meson-baryon scattering. The dashed line on the left denotes the lowest mass of the target hadron ($\text{min}\{M_i\}$), the mass of the nucleon; the dashed line on the right stands for the lowest threshold energy of the $\pi \Sigma$ ($\text{min}\{M_i+m_i\}$).

Figure 3

Deviations of the effective interactions from the Weinberg-Tomozawa term $\Delta V_{\mathit{ii}}(\sqrt{s})$ defined in Eq. (32), (a) $S=-1$ channels, (b) enlargement of panel (c), (c) $S=0$ channels. The channels 1–4 correspond to $\overline{K}N,\pi \Sigma ,\eta \Lambda$, and $K\Xi$ for $S=-1$ channels, and to $\pi N,\eta N,K\Lambda$, and $K\Sigma$ for $S=0$ channels, respectively.

Figure 4

Pole positions of the meson-baryon scattering amplitudes. The triangles stand for the pole positions with the phenomenological amplitude; crosses denote the pole positions in the natural renormalization with the WT interaction. $z_1^{{\Lambda }^{*}}$ and $z_2^{{\Lambda }^{*}}$ are the poles for $\Lambda (1405)$ in the $S=-1$ scattering amplitude, and $z^{N^{*}}$ is the pole for $N(1535)$ in the $S=0$ amplitude.