Abstract
The scattering problem of the \(uudd\bar{s}\) system, in the standard non-relativistic quark model of Isgur-Karl, is solved for the first time, by treating the large five-body model space, including the NK scattering channel, accurately with the Gaussian expansion method and the Kohn-type coupled-channel variational method. The calculated NK scattering phase shift shows no resonance in the energy region of the reported pentaquark Θ+(1540) that is, at 0–500 MeV above the NK threshold (1.4–1.9 GeV in mass). The phase shift does show two resonances just above 500 MeV: a broad \(\frac{1}{2}\)+ resonance with a width of Γ ∼ 110 MeV located at ∼ 520 MeV (∼ 2.0 GeV in mass) and a sharp \(\frac{1}{2}\)− resonance with Γ = 0.12 MeV at 540 MeV.
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