Are the pentaquark sum rules reliable? *

We rewiew and scrutinize the existing mass determinations of the pentaquarks from the exponential Laplace Sum Rules (LSR). We do not find any sum rule window for extracting optimal and reliable results from the LSR, due to the unusual slow convergence of the OPE and to the exceptional important role of the QCD continuum into the spectral function in this channel. Instead, we use in this channel, for the first time, Finite Energy Sum Rules (FESR), which exhibit a nice stability in the QCD continuum threshold tc, at which one can extract, with a good accuracy, the mass of the lowest resonance. Including the D = 7, 9 condensate contributions in the OPE, we obtain MΘ = (1513 ± 114) MeV, and the corresponding residue λΘ2 ∼ -(0.14 ∼ 0.49) × 10−9 GeV12, which favours the I = 0, J = ½, and negative parity S-wave interpretation of the Θ(1540). However, our analysis indicates a degeneracy between the unmixed I = 0 and I = 1 S-wave states. In the I = 0, J = ½, P-wave channel, we obtain, for the P-resonance, Mp ∼ (1.99 ± 0.19) GeV and λP ≈-(0.7 ∼ 7.1) × 10−9 GeV14, which we expect to be discovered experimentally. Our results also suggest that some intuitive choices of the continuum threshold used in the LSR literature are inconsistent with the FESR results. Finally, a study of the Θ-K–N coupling using a vertex sum rule shows that, for the I = 0, S-wave channel, the leading OPE contributions only start to order αs2; in the chiral limit ms = 0, indicating that the Θ is very narrow.