Pentaquark baryon in anisotropic lattice QCD

The pentaquark (5Q) baryon is studied in anisotropic quenched lattice QCD with renormalized anisotropy $a_s/a_t=4$ for a high-precision mass measurement. The standard Wilson action at $\beta =5.75$ and the $O(a)$ improved Wilson quark action with $\kappa =0.1210(0.0010)0.1240$ are employed on a ${12}^3\times 96$ lattice. Contribution of excited states is suppressed by using a smeared source. We investigate both the positive- and negative-parity 5Q baryons with $I=0$ and spin $J=1/2$ using a non-NK-type interpolating field. After chiral extrapolation, the lowest positive-parity state is found to have a mass, $m_{5\mathrm{Q}}=2.25\mathrm{G}\mathrm{e}\mathrm{V}$, which is much heavier than the experimentally observed ${\Theta }^{+}(1540)$. The lowest negative-parity 5Q state appears at $m_{5\mathrm{Q}}=1.75\mathrm{G}\mathrm{e}\mathrm{V}$, which is near the s-wave NK threshold. To distinguish spatially-localized 5Q resonances from NK-scattering states, we propose a new general method imposing a “Hybrid Boundary Condition (HBC),” where the NK threshold is artificially raised without affecting compact five-quark states. The study using the HBC method shows that the negative-parity state observed on the lattice is not a compact 5Q state but an s-wave NK-scattering state.