Spin3/2pentaquarks in anisotropic lattice QCD

High-precision mass measurements of a pentaquark (5Q) ${\Theta }^{+}$ in the $J^P=3/2^{\pm }$ channels are performed in anisotropic quenched lattice QCD. A large number of gauge configurations ($N_{\mathrm{conf}}=1000$) are prepared for the standard Wilson gauge action at $\beta =5.75$ and the $O(a)$ improved Wilson (clover) quark action is employed for $\kappa =0.1210(0.0010)0.1240$ on a ${12}^3\times 96$ lattice with the renormalized anisotropy as $a_s/a_t=4$. The Rarita-Schwinger formalism is adopted for interpolating fields. We examine several interpolating fields with isospin $I=0$, such as (a) the $N{K}^{*}$-type, (b) the color-twisted $N{K}^{*}$-type, and (c) the diquark-type operators. After chiral extrapolation, we obtain massive states, $m_{5\mathrm{Q}}\simeq 2.1–2.2\mathrm{GeV}$ in $J^P=3/2^{-}$, and $m_{5\mathrm{Q}}=2.4–2.6\mathrm{GeV}$ in $J^P=3/2^{+}$. Analyses using the hybrid boundary condition method are performed to determine whether these states are compact 5Q resonances or two-hadron scattering states. No compact 5Q resonance state is found below 2.1 GeV.