Low-lying $\Lambda$ Baryons with spin 1/2 in Two-flavor Lattice QCD

Low-lying $\Lambda$ baryons with spin 1/2 are analyzed in full (unquenched) lattice QCD. We construct $2 \times 2$ cross correlators from flavor SU(3) "octet" and "singlet" baryon operators, and diagonalize them so as to extract information of two low-lying states for each parity. The two-flavor CP-PACS gauge configurations are used, which are generated in the renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved quark action. Three different $\beta$'s, $\beta = 1.80$, 1.95 and 2.10, are employed, whose corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each cutoff, we use four hopping parameters, ($\kappa_{\rm val}, \kappa_{\rm sea}$), which correspond to the pion masses ranging about from 500 MeV to 1.1 GeV. Results indicate that there are two negative-parity $\Lambda$ states nearly degenerate at around 1.6 GeV, while no state as low as $\Lambda (1405)$ is observed. By decomposing the flavor components of each state, we find that the lowest (1st-excited) negative-parity state is dominated by flavor-singlet (flavor-octet) component. We also discuss meson-baryon components of each state, which has drawn considerable attention in the context of multi-quark pictures of $\Lambda (1405)$.