The $1s$ level shift in kaonic deuterium was calculated using Coulomb Sturmian expansion of Faddeev equations. The convergence of the method yields an $\sim\ 1\ eV$ accuracy for the level shifts. We used three different, realistic, multichannel $\bar{K}N$ interactions reproducing all known experimental two-body $\bar{K}N$ data. The different results suggest, that the level shift should be in the range $ΔE\sim(800\pm30)-(480\pm20){\rm i}\ \ eV$. The (almost) exact level shifts were compared with values, given by the commonly used approximations.
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.
A new evaluation of the $1s$ level shift and width of kaonic deuterium is presented based on an accurate $\bar{K}NN$ three-body calculation, using as input a realistic antikaon-nucleon interaction constrained by the SIDDHARTA kaonic hydrogen data. The three-body Schrödinger equation is solved with a superposition of a large number of correlated Gaussian basis functions extending over distance scales up to several hundred fm. The resulting energy shift and width of the kaonic deuterium $1s$ level are $E\simeq 0.67$ keV and $Γ\simeq 1.02$ keV, with estimated uncertainties at the 10% level.
Motivated by the precise measurement of the $1S$ level shift of kaonic hydrogen, we perform accurate three-body calculations for the spectrum of kaonic deuterium using a realistic antikaon-nucleon ($KN$) interaction. In order to describe both short- and long-range behavior of the kaonic atomic states, we solve the three-body Schrödinger equation with a superposition of a large number of correlated Gaussian basis functions covering distances up to several hundreds of fm. Transition energies between $1S$, $2P$ and $2S$ states are determined with high precision. The complex energy shift of the $1…
Exotic deuterium and helium are discussed. The S, P and D levels of antiprotonic and kaonic atoms are calculated. Absorptive, subthreshold antiproton-nucleon amplitudes are extracted from experimental data and compared to model calculations. The existence of a quasi-bound state in the antiproton-nucleon system is indicated. In the kaonic atoms some effects of the Sigma(1385) resonance are evaluated.
Faddeev calculations of the $\bar{K}NN$ system with chirally-motivated $\bar{K}N$ interaction. I. Low-energy $K^- d$ scattering and antikaonic deuterium
The anti-kaon nucleon scattering lengths resulting from a Hamiltonian effective field theory analysis of experimental data and lattice QCD studies are presented. The same Hamiltonian is then used to compute the scattering length for the $K^- d$ system, taking careful account of the effects of recoil on the energy at which the $\bar{K}N$ T-matrices are evaluated. These results are then used to estimate the shift and width of the $1S$ levels of anti-kaonic hydrogen and deuterium. The $K^- p$ result is in excellent agreement with the SIDDHARTA measurement. In the $K^- d$ case the imaginary part o…
We present our latest calculations of $K^-$-nuclear quasi-bound states using a self-consistent scheme for constructing $K^-$-nuclear potentials from various subthreshold chirally inspired $\bar{K}N$ scattering amplitudes. We consider in-medium versions of the scattering amplitudes taking into account Pauli blocking in the intermediate states. The resulting $K^-$ binding energies as well as the widths exhibit the same A dependence, however, the binding energies strongly depend on the model used.
Using separable potentials for $\bar{K}N-πΣ$ interaction, we investigated four-body kaonic nuclear systems such as $K^{-}ppn$ and $K^{-}K^{-}pp$, with the Faddeev AGS method in the momentum representation. The Faddeev calculations are based on the quasi-particle method and the method of the energy dependent pole expansion was used to obtain the separable representation for the integral kernels in the three- and four-body equations. Different types of $\bar{K}N-πΣ$ potentials based on phenomenological and chiral SU(3) approach are used and it was shown that the kaonic nuclear systems under cons…
The energy spectra of light-mass kaonic nuclei were investigated using the theoretical framework of the $0s$-orbital model with zero-range $\bar{K} N$ and $\bar{K}\bar{K}$ interactions of effective single-channel real potentials. The energies of the $\bar{K} NN$, $\bar{K} NNN$, $\bar{K} NNNN$, $\bar{K}\bar{K} N$, and $\bar{K}\bar{K} NN$ systems were calculated in the cases of weak- and deep-binding of the $\bar{K} N$ interaction, which was adjusted to fit the $Λ(1405)$ mass with the energy of the $\bar{K} N$ bound state. The results qualitatively reproduced the energy systematics of kaonic nuc…
The kaonic clusters $K^{-}K^{-}p$ and $ppK^{-}$ are described based on the configuration space Faddeev equations for $AAB$ system. The $AB$ interaction is given by isospin-dependent potentials. For this isospin model, we show that the relation $\left\vert E_{3}(V_{AA}=0)\right\vert~<~2\left\vert E_{2}\right\vert$ is satisfied when $E_{2}$ is the binding energy of the $AB$ subsystem and $E_{3}(V_{AA}=0)$ is the three-body binding energy when interaction between identical particles is omitted, $V_{AA}=0$. For the $NN{\bar K}$ system, taking into account weak attraction of $NN$ interaction the re…
Strong interaction energy shifts and widths in kaonic atoms are calculated for the first time using microscopic $K^- N$ + $K^- NN$ potentials derived from $K^- N$ scattering amplitudes constructed within SU(3) chiral coupled-channels models of meson-baryon interactions. The in-medium modifications of the free-space amplitudes due to the Pauli correlations are taken into account. The $K^-N+K^-NN$ potentials evaluated for 23 nuclear species are confronted with kaonic atoms data. The description of the data significantly improves when the $K^-NN$ absorption is included. To get $χ^2$ as low as for…
$\bar K$-nuclear bound systems, kaonic nuclei, have been widely discussed as products of the strongly attractive $\bar K N$ interaction in $I = 0$ channels. Recently, we demonstrated that kaonic nuclei can be produced via in-flight $(K^-,N)$ reactions using the low-momentum DC kaon beam at the J-PARC E15 experiment. We observed the simplest kaonic nuclei, $K^-pp$, having a much deeper binding energy than normal nuclei. For further studies, we have proposed a series of experimental programs for the systematic investigation of light kaonic nuclei, from $\bar K N$ ($Λ(1405)$) to $\bar K NNNN$. In…
New calculations of the quasi-bound state positions in $K^{-}K^{-}pp$ kaonic nuclear cluster are performed using non-relativistic four-body Faddeev-type equations in AGS form. The corresponding separable approximation for the integral kernels in the three- and four-body kaonic clusters is obtained by using the Hilbert-Schmidt expansion procedure. Different phenomenological models of $\bar{K}N-πΣ$ potentials with one- and two-pole structure of $Λ$(1405) resonance and separable potential models for $\bar{K}$-$\bar{K}$ and nucleon-nucleon interactions, are used. The dependence of the resulting fo…
We performed self-consistent calculations of $K^-$-nuclear quasi-bound states using a single-nucleon $K^-$ optical potential derived from chiral meson-baryon coupled-channel interaction models, supplemented by a phenomenological $K^-$ multinucleon potential introduced recently to achieve good fits to kaonic atom data [1]. Our calculations show that the effect of $K^-$ multinucleon interactions on $K^-$ widths in nuclei is decisive. The resulting widths are considerably larger than corresponding binding energies. Moreover, when the density dependence of the $K^-$-multinucleon interactions deriv…
We propose and examine a new high-density composite of $Λ^* \equiv K^-p = (s \bar{u}) \otimes (uud)$, which may be called {\it Kaonic Proton Matter (KPM)}, or simply, {\it $Λ^* $-Matter}, where substantial shrinkage of baryonic bound systems originating from the strong attraction of the $(\bar{K}N)^{I=0}$ interaction takes place, providing a ground-state neutral baryonic system with a huge energy gap. The mass of an ensemble of $(K^-p)_m$, where $m$, the number of the $K^-p$ pair, is larger than $m \approx 10$, is predicted to drop down below its corresponding neutron ensemble, $(n)_m$, since …
$K^-$ optical potentials relevant to calculations of $K^-$ nuclear quasi-bound states were developed within several chiral meson-baryon coupled-channel interaction models. The applied models yield quite different $K^-$ binding energies and widths. Then, the $K^-$ multinucleon interactions were incorporated by a phenomenological optical potential fitted recently to kaonic atom data. Though the applied $K^-$ interaction models differ significantly in the $K^-N$ subthreshold region, our self-consistent calculations of kaonic nuclei across the periodic table lead to conclusions valid quite general…
The strong interaction between an antikaon and a nucleon is at the origin of various interesting phenomena in kaon-nuclear systems. In particular, the interaction in the isospin $I=0$ channel is sufficiently attractive to generate a quasi-bound state, the $Λ(1405)$ resonance, below the $\bar{K}N$ threshold. Based on this picture, it may be expected that the $\bar{K}N$ interaction also generates quasi-bound states in kaon-nuclear systems, sometimes called kaonic nuclei. At the same time, the $\bar{K}N$ quasi-bound picture of the $Λ(1405)$ is also related to the discussion of hadronic molecules …
Nuclear system with antikaons, so-called kaonic nuclei, has been a longstanding issue in strange nuclear physics and hadron physics, because they might have exotic nature; In particular, they could be a doorway to the dense matter due to the strong attraction between antikaon and nucleon. Among kaonic nuclei, the three-body system composed of two protons and a single $K^-$ meson, $K^-pp$, is the most essential. In this article, we will report on the recent situation of $K^-pp$ studies in both theoretical and experimental sides. Afterwards, we will explain our latest study of the $K^-pp$ with a…
Three-body $AAB$ model for the $NN{\bar K}(s_{NN}=0)$ kaonic cluster is considered based on the configuration space Faddeev equations. Within a single-channel approach, the difference between masses of nucleons and kaons and the charge independence breaking of nucleon-nucleon interaction are taken into consideration. We definite the particle configurations in the system according to the particle masses and pair potentials. There are two sets of the particle configurations, $ ppK^-$, $np \bar{K^0}$ and $nn {\bar K}^0$, $npK^-$, charged and neutral. The three-body calculations are performed by a…
本文从势模型和树近似下的弱二体介子交换流出发，从有效场论出发，研究了氘中负μ介子俘获率的模型依赖性.从$N Δπρωa_1$系统的硬π手征拉格朗日量导出了树单玻色子交换流。如果与单玻色子交换势一起构建，则可以一致地计算捕获率。另一方面，在重子手征微扰理论中构造的有效场论电流包含一个低能常数$\hat d ^R$，它不能从单粒子水平的数据中提取，也不能从第一原理中确定。通过对双峰跃迁速率结果的比较分析，我们可以提取出常数$\hat d ^R$。
Kaonic nuclei (nuclear system with anti-kaons) have been an interesting subject in hadron and strange nuclear physics, because the strong attraction between anti-kaon and nucleon might bring exotic properties to that system. In this article, we investigate $K^-pp$ as a prototype of kaonic nuclei. Here, $K^-pp$ is a three-body resonant state in the $\bar{K}NN$-$πYN$ coupled channels. ($Y$=$Λ$, $Σ$) To treat resonant states in a coupled-channel system properly, we propose newly a coupled-channel complex scaling method combined with the Feshbach projection (ccCSM+Feshbach method). In this method,…
We have investigated the most essential kaonic nucleus "$K^-pp$" as a resonant state of the $\bar{K}NN$-$πΣN$-$πΛN$ coupled channel system using a chiral SU(3)-based $\bar{K}N$ potential. We treat the "$K^-pp$" resonance adequately with a fully coupled-channel complex scaling method (full ccCSM). Self-consistency needs to be considered for the energy dependence of the chiral SU(3)-based potential. In the present study, we propose a simple prescription for the treatment of self-consistency, considering the {\it averaged threshold} and {\it averaged binding energy of mesons}. With this prescript…
