arXiv subjects
Publications and source records attributed to N. V. Shevchenko.
We studied the level shifts in the $K^- p$ system caused by the interplay of strong nuclear and long range Coulomb potentials. We observed a level rearrangement in the system and found that the $1s$ shift of kaonic hydrogen is in fact ``attractive''. In addition, we demonstrated that absorption in the strong antikaon-nucleon interaction does not destroy the level rearrangement.
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.
The mini proceedings of the "Fourth International Workshop on the Extension Project for the J-PARC Hadron Experimental Facility (HEF-ex 2024) [https://kds.kek.jp/event/46965]" held at J-PARC, February 19-21, 2024, are presented. The workshop was devoted to discussing the physics case that connects both the present and the future Hadron Experimental Facility at J-PARC, covering a wide range of topics in flavor, hadron, and nuclear physics related to both experimental and theoretical activities being conducted at the facility.
Characteristics of the quasi-bound state in the $K^- pp$ system strongly depend on the model of antikaon-nucleon interaction and weakly - on the nucleon-nucleon potential. In the present paper, dynamically exact Faddeev-type calculations with coupled $\bar{K}NN$ and $πΣN$ were performed using different models of the $ΣN$ and $πN$ interactions to study the influence of these "less important" interaction on the three-body result. In addition, dynamically exact three-body Faddeev-type AGS calculations with three coupled particle channels $\bar{K}NN - πΣN - πΛN$ were performed.
The paper is devoted to the $\bar{K}NNN$ system, which is an exotic system consisting of an antikaon and three nucleons. Dynamically exact four-body Faddeev-type equations were solved and characteristics of the quasi-bound state in the system were evaluated. Three antikaon-nucleon and three nucleon-nucleon potentials were used, so the dependence of the four-body pole positions on the two-body interaction models was studied. The resulting binding energies $B^{\rm Chiral}_{K^-ppn} \sim 30.5 - 34.5$ MeV obtained with chirally motivated and $B^{\rm SIDD}_{K^-ppn} \sim 46.4 - 52.0$ MeV obtained with phenomenological antikaon-nucleon potentials are close to those obtained for the $K^- pp$ system with the same $\bar{K}N$ and $NN$ potentials, while the four-body widths $Γ_{K^- ppn} \sim 38.2 - 50.9$ MeV are smaller.
Accuracy of "corrected Deser" and "summed up Deser" formulas was checked for the $K^- p$ and $K^- d$ systems. It was found that the last one is much more accurate and should be used for connection the $1s$ level shift to the corresponding scattering length.
It was found that $NN$ 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 the $\bar{K}NN - πΣN$ 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).
The paper is devoted to the $\bar{K}NNN$ system, consisting of an antikaon and three nucleons. Four-body Faddeev-type AGS equations are being solved in order to find possible quasi-bound state in the system.
The paper contains a review of the exact or accurate results achieved in the field of the three-body antikaon-nucleon physics. Different states and processes in $\bar{K}NN$ and $\bar{K}\bar{K}N$ systems are considered. In particular, quasi-bound states in $K^- pp$ and $K^- K^- p$ systems were investigated together with antikaonic deuterium atom. Near-threshold scattering of antikaons on deuteron, including the $K^- d$ scattering length, and applications of the scattering amplitudes are also discussed. All exact three-body results were calculated using some form of Faddeev equations. Different versions of $\bar{K}N$, $ΣN$, $\bar{K}\bar{K}$, and $NN$ potentials, specially constructed for the calculations, allowed investigation of the dependence of the three-body results on the two-body input. Special attention is paid to the antikaon-nucleon interaction, being the most important for the three-body systems. Approximate calculations, performed additionally to the exact ones, demonstrate accuracy of the commonly used approaches.
Dynamically exact calculations of a quasi-bound state in the $\bar{K}\bar{K}N$ three-body system are performed using Faddeev-type AGS equations. As input two phenomenological and one chirally motivated $\bar{K}N$ potentials are used, which describe the experimental information on the $\bar{K}N$ system equally well and produce either a one- or two-pole structure of the $Λ(1405)$ resonance. For the $\bar{K}\bar{K}$ interaction separable potentials are employed that are fitted to phase shifts obtained from two theoretical models. The first one is a phenomenological $\bar{K}\bar{K}$ potential based on meson exchange, which is derived by SU(3) symmetry arguments from the Jülich $ππ- \bar{K} K$ coupled-channels model. The other interaction is a variant of the first one, which is adjusted to the $KK$ s-wave scattering length recently determined in lattice QCD simulations. The position and width of the $\bar{K}\bar{K}N$ quasi-bound state is evaluated in two ways: (i) by a direct pole search in the complex energy plane and (ii) using an "inverse determinant" method, where one needs to calculate the determinant of the AGS system of equations only for real energies. A quasi-bound state is found with binding energy $B_{\bar{K}\bar{K}N} = 12 - 26$ MeV and width $Γ_{\bar{K}\bar{K}N} = 61 - 102$ MeV, which could correspond to the experimentally observed $Ξ(1950)$ state.
The first calculation of kaonic deuterium $1s$ level shift using Faddeev-type equations was performed. The obtained results were compared with commonly used approximate approaches.
We strongly doubt the claimed priority of this work as the first full three-body calculation of the considered reaction.
New calculations of the quasi-bound state in the $K^- pp$ system using Faddeev-type equations in AGS form with coupled $\bar{K}NN$ and $πΣN$ channels were performed. A chiral $\bar{K}N$ potential together with phenomenological models of $\bar{K}N$ 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 $\sim 32$ MeV with the chirally motivated and $47 - 54$ MeV with the phenomenological $\bar{K}N$ potentials. The width is about $50$ MeV for the two-pole models of the interaction, while the one-pole potential gives $\sim 65$ MeV width. The question of using an energy dependent potential in few-body 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.
A chirally-motivated coupled-channel $\bar{K}N$ potential, reproducing all low-energy experimental data on $K^- p$ scattering and kaonic hydrogen and suitable for using in accurate few-body calculations, was constructed. The potential was used for calculations of low-energy amplitudes of the elastic $K^- d$ scattering using Faddeev-type AGS equations with coupled $\bar{K}NN$ and $πΣN$ channels. A complex $K^- - d$ potential reproducing the three-body $K^- d$ amplitudes was constructed and used for calculation of $1s$ level shift and width of kaonic deuterium. The predicted shift $ΔE_{1s}^{K^- d} \sim -830$ eV and width $Γ_{1s}^{K^- d} \sim 1055$ eV are close to our previous results obtained with phenomenological $\bar{K}N$ potentials.
We calculated the $1s$ level shifts and widths of kaonic deuterium, corresponding to accurate results on near-threshold antikaon - deuteron scattering. The Lippmann-Schwinger eigenvalue equation with a strong $K^- - d$ and Coulomb potentials was solved. The two-body $K^- - d$ potentials reproduce the near-threshold elastic amplitudes of $K^- d$ scattering obtained from the three-body Alt-Grassberger-Sandhas equations with the coupled channels using four versions of the $\bar{K}N - πΣ$ potentials. Both new $\bar{K}N - πΣ$ potentials reproducing the very recent SIDDHARTA data on kaonic hydrogen and our older potentials reproducing KEK data have one- or two-pole versions of the $Λ(1405)$ resonance and reproduce experimental data on $K^- p$ scattering.
We investigated the dependence of the $K^- d$ scattering length on models of $\bar{K}N$ interaction with one or two poles for $Λ(1405)$ resonance. The $\bar{K}NN - πΣN$ system is described by coupled-channel Faddeev equations in AGS form. Our new two-body $\bar{K}N - πΣ$ potentials reproduce all existing experimental data on $K^- p$ scattering and kaonic hydrogen atom characteristics. New models of $ΣN - ΛN$ interaction were also constructed. Comparison with several approximations, usually used for scattering length calculations, was performed.
New strong coupled-channel $\bar{K}N - πΣ$ potential, reproducing all existing experimental data and suitable for using in an accurate few-body calculations, is constructed. Isospin breaking effects of direct inclusion of the Coulomb interaction and using of physical masses in calculations are investigated. The $1 s$ level shift and width of kaonic hydrogen, consistent with the scattering data, was obtained and the corresponding exact strong $K^- p$ scattering length was calculated. One- and two-pole form of $Λ(1405)$ resonance was considered.
It is argued, that adjusting strong potentials directly to observed hadronic atom level shifts may lead to significantly different scattering lengths, than those, predicted by the Deser formula. On the example of the 1s level shift of kaonic hydrogen it is demonstrated, that the usually adopted Deser values deduced from the two recent measurements in KEK and by the DEAR Collaboration $a_D({\rm KEK}) = 0.78 - 0.49i$ fm and $a_D({\rm DEAR}) = 0.47 - 0.3i$ fm should be replaced by $a_s({\rm KEK})\simeq 0.85 - 0.62i$ fm and $a_s({\rm DEAR})\simeq 0.49 - 0.35i$ fm, correspondingly.