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

Scattering problem of the uudds¯ system in the standard nonrelativistic 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 two-body interaction that reproduces observed properties of ordinary baryons and mesons is applied to the pentaquark system with no additional adjustable parameter. The resulting five-body wave function has the correct asymptotic form in its scattering-channel component and describes qq and qq¯ correlations properly. The 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). Instead, the phase shift does show two resonances just above 500 MeV: a broad 12+ resonance with a width of Γ∼110MeV located at ∼520MeV (∼2.0GeV in mass) and a sharp 12− resonance with Γ=0.12MeV at 540 MeV. Properties of these states are discussed.