Five-body calculation of resonance and scattering states of pentaquark system

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Scattering problem of the uudd s system, in the standard non-relativistic quark model of Isgur-Karl, is solved for the first time, by treating the large five-body modelspace including the NK scattering channel accurately with the Gaussian expansion method and the Kohn-type coupled-channel variational method. The two-body interaction that reproduces observed properties of ordinary baryons and mesons is applied to the pentaquark system with no additional adjustable parameter. The five-body wave function calculated has the correct asymptotic form in its the scattering-channel component and describes qq and q q correlations properly. The NK scattering phase shift calculated 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 110 MeV located at 520 MeV (2.0 GeV in mass) and a sharp 1/2- resonance with Γ=0.12 MeV at 540 MeV. Properties of these states are discussed.