Isospin Effect in Three-Body Kaonic Clusters

I. Filikhin, B. Vlahovic

Published 2017-09-22Version 1

The kaonic clusters $K^{-}K^{-}p$ and $ppK^{-}$ are studied based on the configuration space Faddeev equations for $AAB$ system. The relation between the doubled binding energy of the $AB$ subsystem $2E_{2}$ and the three-body binding energy $E_{3}(V_{AA}=0)$, when the interaction between the identical particles is omitted, is considered. The isospin-less model leads to the relation $\left\vert E_{3}(V_{AA}=0)\right\vert >2\left\vert E_{2}\right\vert$. For the kaonic clusters, described within isospin formalism, the relation $\left\vert E_{3}(V_{AA}=0)\right\vert~<~2\left\vert E_{2}\right\vert$ is satisfied. Thus, the binding energy of the kaonic system $NN{\bar K}$ is limited by $|E_3|\le |2E_2|$ due to a weak attraction of the spin singlet $NN$ interaction.