On a Quasi-Bound State in the $$\pmb {{ K^- d}}$$ System Caused by Strong Interactions

Abstract

It was found that N N potential could influence the results of the quasi-bound state search in the K − d system, where the corresponding pole is situated close to the threshold. Three-body Faddeev-type calculations of theK N N − πΣ N system performed with a new model of nucleon-nucleon interaction predict the existence of the quasi-bound K − d state caused by strong interactions. Its binding energy is small (1-2 MeV), while the width is comparable with the width of the K − pp quasi-bound state (40-60 MeV).

Particle configurations in the $NN\bar K$ system

“…For example, calculated value |E 3 | reported in Ref. [25] is about 46.6 MeV for phenomenological KN potential with two-pole Λ(1405) structure (see also Ref. [39]).…”

Four-body Faddeev-type calculation of the $\bar{K}NNN$ system

“…The quasi-bound state caused by strong interactions only (in addition to an atomic state, kaonic deuterium) can exist in the 𝐾 − 𝑑 system similarly to the 𝐾 − 𝑝 𝑝 system with a much smaller binding energy(1 − 2 MeV) than the binding energy of the 𝐾 − 𝑝 𝑝 quasi-bound state. The widths of the 𝐾 − 𝑑 and 𝐾 − 𝑝 𝑝 states are comparable, see [9].…”

“…As for the nucleon-nucleon interaction, we constructed a new version of the two-term separable 𝑁 𝑁 potential, its form and parameters are described in [9]. The potential reproduces Argonne v18 𝑁 𝑁 phase shifts at low energies up to 500 MeV, so that it is repulsive at short distances.…”

“…The three-body AGS equations were solved with three separable K 𝑁 potentials, mentioned above. In particular, a quasi-bound state exists in the 𝐾 − 𝑝 𝑝 system ( K 𝑁 𝑁 with spin zero), its binding energy and width were evaluated in our previous works and recalculated recently with the new model of the 𝑁 𝑁 interaction [9].…”

“…Binding energy 𝐵 𝐾 − 𝑝 𝑝𝑛 (MeV) and width Γ 𝐾 − 𝑝 𝑝𝑛 (MeV) of the quasi-bound state in the 𝐾 − 𝑝 𝑝𝑛 system calculated with three K 𝑁 potentials and new two-term separable 𝑉 𝑁 𝑁 .𝐾 − 𝑝 𝑝𝑛 − K− 𝑛𝑛𝑝 system has a smaller binding energy (16 − 36 MeV) than the similar state in the three-body 𝐾 − 𝑝 𝑝 system[9]. The width of the four-body 𝐾 − 𝑝 𝑝𝑛 state is larger than the width of 𝐾 − 𝑝 𝑝 and 𝐾 − 𝑑 quasi-bound states obtained with two-pole K 𝑁 potentials 𝑉 2,SIDD K 𝑁 and 𝑉 Chiral K 𝑁 and smaller, when the one-pole 𝑉1,SIDD …”