Faddeev calculations of theK¯NNsystem with a chirally motivatedK¯Ninteraction. II. The

J. Révai

¹

,

Н. В. Шевченко

²

Abstract

New calculations of the quasi-bound state in the K − pp system using Faddeev-type equations in AGS form with coupledKN N and πΣN channels were performed. A chiralKN potential together with phenomenological models ofKN interaction with one-and two-pole structure of the Λ(1405) resonance were used. All three potentials reproduce experimental data on low-energy K − p scattering and kaonic hydrogen with the same level of accuracy. New method of calculating the subthreshold resonance position and width in a three-body system was proposed and used together with the direct search of the resonance pole. We obtained binding energy of the K − pp quasi-bound state ∼ 32 MeV with the chirally motivated and 47 − 54 MeV with the phenomenologicalKN potentials. The width is about 50 MeV for the two-pole models of the interaction, while the onepole potential gives ∼ 65 MeV width. The question of using an energy dependent potential in fewbody calculations is discussed in detail. It is shown that "self-consistent" variational calculations using such a potential are unable to produce a reasonable approximation to the exact result.

Deeply quasi-bound state in single- and double- $\bar{K}$ K ¯ nuclear clusters

“…It can be seen from table III that our calculated binding energies are very close to the other results obtained in [7] and [18] for K − pp and K − K − p systems using the sameKN −πΣ potentials within the coupled-channel Faddeev approach.…”

“…The first experimental evidence concerning K − pp was observed in the stopped K − on 6,7 Li and 12 C targets [12] by FINUDA collaboration at DAΦNE. An exclusive analysis of the p + p → X + K + , X → p + Λ experiment at Saclay for the pp reaction at 2.85 GeV [13] indicated a large peak both in the Λp invariant-mass and K + missing-mass spectra, which had been predicted in the theoretical works [14,15].…”

Antistrange meson-baryon interaction in hot and dense nuclear matter

“…This analysis was strongly criticized [34] due to the unrealistic treatment of theKN interaction. Recent improved calculations using different few-body methods with diverseKN input [35][36][37][38][39][40][41][42][43][44] predict few-nucleon kaonic states with large widths, although the predicted binding energies and widths differ substantially from one model to the other. Thus, the experimental quest for such deeply bound kaonic states is an active field of research [45][46][47][48][49][50][51], that will allow to further constrain thē KN interaction in the near future.…”

\(\bar{K}\)N Interactions in the Nuclear Medium and \(\bar{K}\) Nuclear Quasi-Bound States

“…The figure illustrates that the method of solving the 3-body problem (variational or Faddeev) is less important than the choice of the underlying interaction model. The effect of the one-vs. two-pole structure of [20]. Experimental K − pp candidates E27 [21], DISTO [22], FINUDA [23], and OBELIX [24] are shown as well.…”

“…2 denoted by D [13], B [14], Y [15], M [16], and W [17]), and coupled channels genuine three-body Faddeev calculations (IK [18], IS [19], S [12], R1, R2, and RC [20]). The figure illustrates that the method of solving the 3-body problem (variational or Faddeev) is less important than the choice of the underlying interaction model.…”