Anisotropic lattice QCD studies of spin 3/2 penta-quark

Anisotropic lattice QCD results for the penta-quark(5Q) $\Theta^+$ in $J^{P}=3/2^{\pm}$ channel are presented for a high-precision mass measurement using a large number of gauge configurations as $N_{\rm conf}=1000$. The standard Wilson gauge action at $\beta=5.75$ with the renormalized anisotropy as $a_{\rm s}/a_{\rm t} = 4$, and $O(a)$ improved Wilson (clover) quark action with $\kappa=0.1210(0.0010)0.1240$ are employed on a $12^3 \times 96$ lattice. Several Rarita-Schwinger interpolating fields with isospin $I=0$ are examined such as (a) the NK$^*$-type, (b) the (color-)fused NK$^*$-type, (c) a diquark-type. The chiral extrapolation leads to only massive states as $m_{5Q} > 2$ GeV. The analysis with the hybrid BC(HBC) is performed to investigate whether these states are compact 5Q resonances or not. No localized 5Q resonance states are found.