Fine-tuning of the $\bar{K}NN$ and $\bar{K}\bar{K}N$ quasi-bound state calculations

TL;DR

The study tackles kaonic three-body quasi-bound states by employing dynamically exact three-body Faddeev-AGS equations with three coupled channels to include $\bar{K}N$, $\pi\Sigma$, and $\pi\Lambda$ dynamics. It introduces new two-body inputs—three coupled $\bar{K}N-\pi\Sigma-\pi\Lambda$ potentials (one-pole, two-pole, and chirally motivated) along with refined $YN$ and $\pi N$ interactions and a TSN $NN$ potential—to finely tune theoretical predictions. The results show that the one-pole phenomenological potential can reproduce the E15 J-PARC2 $K^-pp$ binding energy and width, while the two-pole and chirally motivated inputs yield different, generally smaller widths; in the $K^-np$ channel a quasi-bound state emerges for all inputs, and the $K^-K^-p$ system typically has smaller binding and width than $K^-pp$ under most potentials. Overall, the work emphasizes the critical role of fully coupled-channel three-body dynamics and carefully calibrated two-body inputs for accurate kaonic-nuclei predictions and their interpretation in experimental kaon-nucleus studies.

Abstract

Fine-tuning of the binding energies and widths of the quasi-bound states in three-body systems consisting of antikaon(s) and nucleon(s) was performed. Dynamically exact three-body Faddeev-type AGS equations with three coupled particle channels were solved for the description of the $\bar{K}NN$ and $\bar{K} \bar{K} N$ systems in different spin states. New models of the antikaon-nucleon and pion-nucleon interactions were constructed, and together with our best versions for the remaining potentials were used as input. The characteristics of the quasi-bound $K^- pp$ state calculated with our new one-pole $\bar{K}N - πΣ- πΛ$ potential reproduces the experimental data from the E15 J-PARC experiment.

Figures (1)

• Figure 1: $K^- p$ elastic and inelastic low-energy cross-sections given by our antikaon-nucleon potentials coupling $\bar{K}N$, $\pi \Sigma$, and $\pi \Lambda$ channels. Straingt line (denoting results calculated with $V^{\rm 1,SIDD-A}_{\bar{K}N - \pi \Sigma - \pi \Lambda}$ potential), long dashed line ($V^{\rm 1,SIDD-B}_{\bar{K}N - \pi \Sigma - \pi \Lambda}$), dash-dash-dot line ($V^{\rm 2,SIDD-A}_{\bar{K}N - \pi \Sigma - \pi \Lambda}$), dot-dot-dash line ($V^{\rm 2,SIDD-B}_{\bar{K}N - \pi \Sigma - \pi \Lambda}$), and dash-dot line ($V^{\rm Chiral}_{\bar{K}N - \pi \Sigma - \pi \Lambda}$) are compared with experimental data Kp2expKp3exp_1Kp3exp_2Kp4expKp5expKp6expKpLASTexp (symbols). A and B versions of the phenomenological one- and two-pole potentials are those with negative or positive $I=1$ strength constants, correspondingly.