  We study spin $\frac12$ hadronic states in quenched lattice QCD to search for
a possible $S=+1$ pentaquark resonance. Simulations are carried out on
$8^3\times 24$, $10^3\times 24$, $12^3\times 24$ and $16^3\times 24$ lattices
at $\beta$=5.7 at the quenched level with the standard plaquette gauge action
and the Wilson quark action. We adopt a Dirichlet boundary condition in the
time direction for the quark to circumvent the possible contaminations due to
the (anti)periodic boundary condition for the quark field, which are peculiar
to the pentaquark. By diagonalizing the $2\times 2$ correlation matrices
constructed from two independent operators with the quantum numbers
$(I,J)=(0,\frac12)$, we successfully obtain the energies of the lowest state
and the 2nd-lowest state in this channel. The analysis of the volume dependence
of the energies and spectral weight factors indicates that a resonance state is
likely to exist slightly above the NK threshold in $(I,J^P)=(0,\frac12^-)$
channel.

High Energy Physics - Lattice;High Energy Physics - Phenomenology;Nuclear Theory