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

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

2007-04-09

arxiv.org/abs/0704.1072v2

Prog.Theor.Phys.Suppl.168:111-114,2007

Physics

Nuclear Physics

Nuclear Theory

4 pages, 4 figures

Scientific paper

10.1143/PTPS.168.111

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $\Theta^+$ in the diquark picture of Jaffe and Wilczek in which $\Theta^+$ 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 $\Theta^+$ can only be obtained with unphysically strong vector mesonic coupling constants.

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