Study of Pentaquark and $\Lambda(1405)$

Abstract

We perform a five-body calculation for pentaquark $(q^4\bar{q})$ state of $\Lambda(1405)$ as well as the three-body calculations for the ground state baryons and the $\Lambda(1405)$, and two-body calculations for mesons. The hamiltonian, which reproduces reasonably well the energies of ground state baryons ($N,\Lambda,\Sigma,\Xi$ and $\Delta$) and mesons ($\pi,K,\rho,K^\ast$), includes kinetic energy of semi-relativistic form, linear confinement potential, and the simplest form of color-magnetic interaction with Gaussian form factor. Flavor symmetry breaking ($m_s> m_{u,d}$) is taken into account. The energy calculated for $(q^4\bar{q})$ state of $\Lambda(1405)$ is lower than the energy for the $(q^3)$ state. The present result suggests that the $\Lambda(1405)$ is a pentaquark-dominated state if the color-magnetic potential plays a leading role of the quark-quark and quark-antiquark interactions.