Four- and Five-Body Scattering Calculations

Abstract

We study the five-quark system $uudd\bar{s}$ in the standard non-relativistic quark model by solving the scattering problem. Using the Gaussian Expansion Method (GEM), we perform the almost precise multi-quark calculations by treating a very large five-body modelspace including the NK scattering channel explicitly. Although a lot of pseudostates (discretized continuum states) with $J^{\pi }={1/2}^{\pm }$ and $J^{\pi }={3/2}^{\pm }$ are obtained within the bound-state approximation, all the states in $1.4-1.85$ GeV in mass around ${\mathrm{\Theta }}^{+}(1540)$ melt into non-resonant continuum states through the coupling with the NK scattering state in the realistic case, i.e., there is no five-quark resonance below 1.85GeV. Instead, we predict a five-quark resonance state of $J^{\pi }={1/2}^{-}$ with the mass of about 1.9GeV and the width of $\Gamma \simeq$ 2.68MeV. Similar calculation is done for the four-quark system $c\bar{c}q\bar{q}$ ($q=u,d$) in connection with X${}^0$(3872).

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