We study the question of whether or not QCD predicts a pentaquark state. We use the improved, fixed point lattice QCD action which has very little sensitivity to the lattice spacing and also allows us to reach light quark masses. The analysis was performed on a single volume of size $(1.8 {rm fm})^3times 3.6 {rm fm}$ with lattice spacing of $a=0.102$ fm. We use the correlation matrix method to identify the ground and excited states in the isospin 0, negative parity channel. In the quenched approximation where dynamical quark effects are omitted, we do not find any evidence for a pentaquark resonance in QCD.
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