Five-body calculation of resonance and scattering states of the uudds̄ system

The scattering problem of the uudds̄ 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 1/2 ⁺ resonance with a width of Γ ∼ 110MeV located at ∼520MeV (∼2.0GeV in mass) and a sharp 1/2^- resonance with Γ = 0.12∈MeV at 540∈MeV.