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

Abstract Scattering problem of the u u d d s ¯ 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 q q ¯ 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 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.