Faddeev calculation of pentaquark $Θ^+$ in the Nambu-Jona-Lasinio model-based diquark picture
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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 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 $Θ^+$ with $ \frac 12^-$ is obtained with a unphysically strong vector mesonic coupling constants.
22 pages, 11 figures, accepted version in Phys. Rev. C. Summary of main changes/corrections: 1. "which only holds at tree level" below the eq. (23) is added. 2. In the last paragraph of p.23 we added a remark that the coupling constant obtained from Lambda mass is different from the estimate as obtained from the meson spectrum
22 pages, 11 figures, accepted version in Phys. Rev. C. Summary of main changes/corrections: 1. "which only holds at tree level" below the eq. (23) is added. 2. In the last paragraph of p.23 we added a remark that the coupling constant obtained from Lambda mass is different from the estimate as obtained from the meson spectrum