ppK- bound states from Skyrmions


The bound kaon approach to the strangeness in the Skyrme model is applied to investigating the possibility of deeply bound ppKβˆ’ppK^- states. We describe the ppKβˆ’ppK^- system as two-Skyrmion around which a kaon field fluctuates. Each Skyrmion is rotated in the space of SU(2) collective coordinate. The rotational motions are quantized to be projected onto the spin-singlet proton-proton state. We derive the equation of motion for the kaon in the background field of two Skyrmions at fixed positions. From the numerical solution of the equation of motion, it is found that the energy of Kβˆ’K^- can be considerably small, and that the distribution of Kβˆ’K^- shows molecular nature of the ppKβˆ’ppK^- system. For this deep binding, the Wess-Zumino-Witten term plays an important role. The total energy of the ppKβˆ’ppK^- system is estimated in the Born-Oppenheimer approximation. The binding energy of the ppKβˆ’ppK^- state is B.E.≃126B.E.\simeq 126 MeV. The mean square radius of the pppp subsystem is ≃1.6\sqrt{}\simeq 1.6 fm.Comment: Oct 2007, 15 pages, 8 figures; added references, corrected typo

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