MOLECULE MODEL FOR KAONIC NUCLEAR CLUSTER $\bar{K}NN$

We analyze the properties of the kaonic nuclear cluster (KNC) [Formula: see text] with the structure [Formula: see text], having the quantum numbers [Formula: see text], and treated as a quasi-bound hadronic molecule state. We describe the properties of the hadronic molecule, or the KNC [Formula: see text], in terms of vibrational degrees of freedom with oscillator wave functions and chiral dynamics. These wave functions, having the meaning of trial wave functions of variational calculations, are parametrized by the frequency of oscillations of the [Formula: see text] pair, which is fixed in terms of the binding energy of the strange baryon resonance Λ(1405), treated as a quasi-bound [Formula: see text] state. The binding energies BX and widths ΓX of the states [Formula: see text] and [Formula: see text], respectively, are calculated in the heavy-baryon approximation by using chiral Lagrangians with meson–baryon derivative couplings invariant under chiral SU (3)× SU (3) symmetry at the tree-level approximation. The results are [Formula: see text] and [Formula: see text] and, where [Formula: see text] and [Formula: see text] are the widths of non-pionic [Formula: see text], NΣ and pionic [Formula: see text] decay modes, calculated for [Formula: see text] and [Formula: see text], respectively.