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Two-Hadron-Irreducible QCD Sum Rule for Pentaquark Baryon

We point out that naive pentaquark correlations function include two-hadron-reducible contributions, which are given by convolution of baryon and meson correlation functions and have nothing to do with pentaquark. We show that the two-hadron-reducible contributions are large in the operator product expansion of the correlation functions of three existing works on the pentaquark. Therefore, it is dangerous to draw a conclusion from the sum rules using naive pentaquark correlation functions with naive ansatz for the spectral function under the dispersion integral. Instead, we propose to use the two-hadron-irreducible correlation function, which is obtained by subtracting the two-hadron-reducible contribution from the naive correlation function. Taking one of the works as an example we demonstrate how drastically the results can change if we remove the two-hadron-reducible part from the naive correlation function. We obtain the result opposite to the original work for the parity of the pentaquark.