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arXiv · 0710.0196

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

H. Mineo·J. A. Tjon·K. Tsushima·Shin Nan 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 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.

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H. Mineo, J. A. Tjon, K. Tsushima, Shin Nan Yang. 2008-04-10. Faddeev calculation of pentaquark $Θ^+$ in the Nambu-Jona-Lasinio model-based diquark picture. https://doi.org/10.1103/physrevc.77.055203

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