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arXiv · 0704.1072

A Faddeev Calculation for Pentaquark $Θ^+$ in Diquark Picture with Nambu-Jona-Lasinio Type Interaction

H. Mineo·J. A. Tjon·K. Tsushima·S. N. Yang
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Abstract

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $Θ^+$ in the diquark picture of Jaffe and Wilczek in which $Θ^+$ is a diquark-diquark-${\bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of ${\bar s}D$ and $D D$. With the use of coupling constants determined from the meson sector, we find that ${\bar s}D$ interaction is attractive while $DD$ interaction is repulsive, and there is no bound $\frac 12^+$ pentaquark state. A bound pentaquark $Θ^+$ can only be obtained with unphysically strong vector mesonic coupling constants.

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H. Mineo, J. A. Tjon, K. Tsushima, S. N. Yang. 2007-10-16. A Faddeev Calculation for Pentaquark $Θ^+$ in Diquark Picture with Nambu-Jona-Lasinio Type Interaction. https://doi.org/10.1143/ptps.168.111

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