The QCD sum rule method is formulated for the strangeness +1 pentaquark baryon with isospin I=0 and spin-parity J^P = 3/2^pm. The spin-3/2 states are considered to be narrower than the spin-1/2 ones, and thus may provide a natural explanation for the experimentally observed narrow width of Theta^+. In order to obtain reliable results in QCD sum rule calculations, we stress the importance of establishing a wide Borel window, where convergence of the operator product expansion and sufficient low-mass strength of the spectral function are guaranteed. To this end, we employ the difference of two independent correlators so that the high-energy continuum contribution is suppressed. The stability of the physical quantities against the Borel mass is confirmed within the Borel window. It is found that the sum rule gives positive evidence for the (I, J^P) = (0, 3/2^+) state with a mass of about 1.4 pm 0.2 GeV, while we cannot extract any evidence for the (0, 3/2^-) state.
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