Negative-parity baryon spectrum in quenched anisotropic lattice QCD

We investigate the negative-parity baryon spectra in quenched lattice QCD. We employ the anisotropic lattice with a standard Wilson gauge and $O\left(a\right)\mathrm{}$ improved Wilson quark actions at three values of lattice spacings with a renormalized anisotropy $\xi {=a}_{\sigma }{/a}_{\tau }=4,$ where $a_{\sigma }$ and $a_{\tau }$ are spatial and temporal lattice spacings, respectively. The negative-parity baryons are measured with the parity projection. In particular, we pay much attention to the lowest SU(3) flavor-singlet negative-parity baryon, which is assigned as the $\Lambda \mathrm{}\left(1405\right)\mathrm{}$ in the quark model. For the flavor octet and decuplet negative-parity baryons, the calculated masses are close to the experimental values of corresponding lowest-lying negative-parity baryons. In contrast, the flavor-singlet baryon is found to be about 1.7 GeV, which is much heavier than the $\Lambda \mathrm{}\left(1405\right).$ Therefore it is difficult to identify the $\Lambda \mathrm{}\left(1405\right)\mathrm{}$ to be the flavor-singlet three-quark state, which seems to support an interesting picture of the pentaquark $\left(udsq\overline{q}\right)$ state or the $N\overline{K}$ molecule for the $\Lambda \mathrm{}\left(1405\right).$