$Λ(1405)$ from lattice QCD

Low-lying $Λ$ baryons with spin 1/2 are analyzed in two-flavor lattice QCD. In order to extract two low-lying states for each parity, we construct $2 \times 2$ cross correlators from flavor SU(3) ``octet'' and ``singlet'' baryon operators, and diagonalize them. Two-flavor CP-PACS gauge configurations are employed, which are generated with the renormalization-group improved gauge action and the ${\mathcal O}(a)$-improved quark action. Simulation are performed at three different $β$'s, $β= 1.80$, 1.95 and 2.10, whose corresponding lattice spacings are $a = 0.2150$, 0.1555 and 0.1076 fm. For each cutoff, we adopt four different hopping parameters, ($κ_{\rm val}, κ_{\rm sea}$). The corresponding pion masses range from about 500 MeV to 1.1 GeV. The results are extrapolated to the physical quark-mass point. Our results indicate that there are two negative-parity $Λ$ states nearly degenerate at around 1.6 GeV, whereas no state as low as $Λ(1405)$ is observed. By extracting the flavor components of each state, we find that the lowest (1st-excited) negative-parity state is dominated by flavor-singlet (flavor-octet) component.

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