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

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 Added by Hirobumi Mineo
 Publication date 2007
  fields
and research's language is English




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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 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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115 - H. Mineo , J.A. Tjon , K. Tsushima 2008
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.
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189 - W. Bentz 2001
Using the Nambu-Jona-Lasinio model to describe the nucleon as a quark-diquark state, we discuss the stability of nuclear matter in a hybrid model for the ground state at finite nucleon density. It is shown that a simple extension of the model to simulate the effects of confinement leads to a scalar polarizability of the nucleon. This, in turn, leads to a less attractive effective interaction between the nucleons, helping to achieve saturation of the nuclear matter ground state. It is also pointed out that that the same effect naturally leads to a suppression of ``Z-graph contributions with increasing scalar potential.
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