ppK- bound states from Skyrmions

TL;DR

This paper investigates the possibility of deeply bound ppK- states using a Skyrme model approach, finding significant binding energy and molecular-like distribution, with the Wess-Zumino-Witten term playing a crucial role.

Contribution

It introduces a novel application of the bound kaon approach to Skyrmions for modeling ppK- states and estimates their binding energy and structure.

Findings

Binding energy of approximately 126 MeV for ppK-

The K- distribution indicates a molecular nature of the system

The Wess-Zumino-Witten term is essential for deep binding

Abstract

The bound kaon approach to the strangeness in the Skyrme model is applied to investigating the possibility of deeply bound $ppK^-$ states. We describe the $ppK^-$ 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 $K^-$ can be considerably small, and that the distribution of $K^-$ shows molecular nature of the $ppK^-$ system. For this deep binding, the Wess-Zumino-Witten term plays an important role. The total energy of the $ppK^-$ system is estimated in the Born-Oppenheimer approximation. The binding energy of the $ppK^-$ state is $B.E.\simeq 126$ MeV. The mean square radius of the $pp$ subsystem is $\sqrt{< r_{pp}^2>}\simeq 1.6$ fm.