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 in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $ frac 12^+$ pentaquark state. Instead, a bound pentaquark $Theta^+$ with $ frac 12^-$ is obtained with a unphysically strong vector mesonic coupling constants.
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 calculat
e 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.
