Λ(1405) as a resonance in the baryon-meson scattering coupled to the $q^3$ state in a quark model

To describe Λ(1405) as a resonance in baryon-meson scattering, we have investigated the $q^3$-$q\overline{q}$ scattering system with the flavor-singlet $q^3(0s){}^2(0p)$ state (the ${\Lambda }^1$ pole). The scattering is treated by the quark cluster model (QCM). The ${\Lambda }^1$ pole is treated as a bound state embedded in the continuum. We have found that a peak appears below the $\mathrm{N}\overline{\mathrm{K}}$ threshold in the spin-$\frac{1}{2}$, isospin-0 channel even if the mass of the ${\Lambda }^1$ pole is above the threshold. This peak disappears when the coupling to the ${\Lambda }^1$ pole is switched off. Using the observed hadron mass in the kinetic part of QCM is also found to be important in reproducing a peak just below the $\mathrm{N}\overline{\mathrm{K}}$ threshold.

Figure 1

Annihilation diagram of the $j$th quark and the $\overline{k}$th antiquark by OGE, where the gluon carries three-momentum $\mathit{k}={\mathit{p}}_j+{\mathit{p}}_{\overline{k}}$ to the $i$th quark.

Figure 2

Phase shift and the mass spectrum of the $\Sigma \pi$ channel for the angular momentum $L=0$ given by the QCM calculation without the ${\Lambda }^1$ pole with the constituent-quark reduced mass, $6m_q/5$.

Figure 3

Phase shift and the mass spectrum of the $\Sigma \pi$ channel for the angular momentum $L=0$ given by the QCM calculation with the ${\Lambda }^1$ pole at $E_{\mathrm{pole}}^{(0)}=160$ MeV and the constituent-quark reduced mass, $6m_q/5$.

Figure 4

Phase shift and the mass spectrum of the $\Sigma \pi$ channel for the angular momentum $L=0$ and the wave function at the resonance. The QCM calculation is performed with the ${\Lambda }^1$ pole at $E_{\mathrm{pole}}^{(0)}=160$ MeV and realistic reduced masses.

Figure 5

The diagonal parts of the $S$ matrix for coupled-channel baryon-meson scattering.

Figure 6

The effect of the channel couplings on the peak.