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

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-s̅ three-body system. The Nambu–Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of s̅ D and DD. With the use of coupling constants determined from the meson sector, we find that s̅ D interaction is attractive in s-wave while the DD interaction is repulsive in the p-wave. With only the lowest three-body channel considered, we do not find a bound 1/2+ pentaquark state. Instead, a bound pentaquark Θ+ with 1/2- is obtained with unphysically strong vector mesonic coupling constants.