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A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark$\Theta^+$ in the diquark picture of Jaffe and Wilczek in which $\Theta^+$ is adiquark-diquark-${\bar s}$ three-body system. Nambu-Jona-Lasinio (NJL) model isused 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 themeson sector, we find that ${\bar s}D$ interaction is attractive in s-wavewhile $DD$ interaction is repulsive in p-wave. With only the lowest three-bodychannel considered, we do not find a bound $ \frac 12^+$ pentaquark state.Instead, a bound pentaquark $\Theta^+$ with $ \frac 12^-$ is obtained with aunphysically strong vector mesonic coupling constants.

Faddeev calculation of pentaquark $\Theta^+$ in the Nambu-Jona-Lasinio model-based diquark picture