KN Interaction Research Articles

The Fourth-Order KN potential Matrix-Element in 3D basis

The aim of this study is to derive the fourth-order KN potential matrix-element. The matrix element is derived in 3D basis. Previous study about the-second order KN interaction shows that the result need to be improved, so we continue the study to the fourth-order. Potential matrix-element is derived from KN Interaction potential which is developed by Büttgen (Nucl. Phys. A506) dan Müller (Nucl. Phys. A513). The meson being exchanged in the fourth-order KN interaction is pion with intermediate state are NK* and ΔK*. Potential matrix-element is formulated from potential on 3D basis. We apply 3D technique in this study as a good alternative to Partial wave technique. That technique does not expand the free state in partial wave so it is useful in high energy scattering. Potential matrix-element derived from this study can be used to calculate differential cross section which can be used to calculate the contribution of pion exchange in KN scattering.

High precision Kaonic Deuterium measurement at the DAΦNE collider: the SIDDHARTA-2 experiment and the SIDDHARTINO run

The kaonic deuterium 2p→1s transition X-ray measurement, a fundamental information needed for a deeper understanding of the Quantum ChromoDynamics (QCD) in the strangeness sector, is still missing. The SIDDHARTA-2 collaboration is now ready to achieve this unprecedented result thanks to the dedicated experimental apparatus that will allow to obtain the values of the kaonic deuterium K-transitions with a precision comparable to the most precise kaonic hydrogen measurement to-date performed by SIDDHARTA in 2009. Both the kaonic hydrogen and kaonic deuterium X-ray spectroscopy measurements of the de-excitation towards the fundamental level are a direct probe on KN interaction at threshold, as opposed to the scattering experiments which need an extrapolation to zero energy. Combining these results through the Deser-Truemann like formula, the isospin-dependent kaon-nucleon scattering lengths can be obtained in a model-independent way. The SIDDHARTA-2 setup is presently installed at the DAΦNE (Double Annular Φ Factory for Nice Experiments) collider of Istituto Nazionale di Fisica Nucleare – Laboratori Nazionali di Frascati and it is ready to perform the challening kaonic deuterium measurement. Thispaper provides an overview on the SIDDHARTA-2 experimental apparatus and a preliminary result of the kaonic helium run, preparatory for the SIDDHARTA-2 data taking campaign, is also presented.

One hadron exchange non-relativistic model for potential

One of the KN Interaction is K+p interaction which one we’re interested in. K+p potential is described as one hadron exchanges. The hadrons being exchanged include scalar meson (σ), vector mesons (ω, ρ ), hyperons (Λ, Σ), and their resonances ( Λ* (1600), Σ*(1385)). This interaction model is derived for non-relativistic calculations within Blankenbecler-Sugar reduction. The values of the potential parameters are fixed by fitting to experimental data of K+p spin-averaged differential cross section for kaon laboratory energies from 88.13 MeV to 3683.22 MeV. Scattering calculations are performed by using a 3D technique without partial wave expansion.

Low Energy KN Interaction in the Fock-Tani Formalism

The Fock-Tani formalism is a first principle method to obtain effective interactions from microscopic Hamiltonian. Originally derived for meson-meson or baryon-baryon scattering, we present the corresponding equations for meson-baryon scattering. In particular we shall obtain the low energy cross sections for the [Formula: see text] channel.

Lightest Kaonic Nuclear Clust

We present our study of kaonic three-body KNN , KNN and KKK and four-body KNNN , and KKNN clusters within the framework of a potential model using the method of hyperspherical functions in momentum representation. To perform a numerical calculations for the bound state energy of the light kaonic system, we use a set of different potentials for the nucleon-nucleon and KN interactions, as well as for the kaon-kaon interaction. The calculations show that a quasibound state energy is not sensitive to the NN interaction, and it shows very strong dependence on the KN potential. We also compare our results with those obtained using different theoretical approaches. The theoretical discrepancies in the binding energy and width for the lightest kaonic system related to the different NN and KN interactions are addressed.

Future projects of light kaonic atom X-ray spectroscopy

X-ray spectroscopy of light kaonic atoms is a unique tool to provide precise information on the fundamental KN interaction at the low-energy limit and the in-medium nuclear interaction of K-. The future experiments of kaonic deuterium strong-interaction shift and width (SIDDHARTA-2 and J-PARC E57) can extract the isospin dependent K-N interaction at threshold. The high-resolution X-ray spectroscopy of kaonic helium with microcalorimeters (J-PARC E62) has the possibility to solve the long-standing potential-strength problem of the attractive K--nucleus interaction. Here, the recent experimental results and the future projects of X-ray spectroscopy of light kaonic atoms are presented.

New precision era of experiments on strong interaction with strangeness at DAFNE/LNF-INFN

The strong-interaction shifts and widths of kaonic hydrogen, deuterium, 3 He, and 4 He were measured in the SIDDHARTA experiment. The most precise values of the shift and width of the kaonic hydrogen 1s state were determined to be ϵ1s = −283 ± 36(stat) ±6(syst) eV and Γ1s = 541 ±89(stat) ±22(syst) eV. The upper limit of the kaonic deuterium Kα yield was found to be ≤ 0.39%. In addition, the shifts and widths of the kaonic 3 He and 4 He 2p states were determined to be ϵ2p( 3 He) = −2 ± 2(stat) ± 4(syst) eV and Γ2p( 3 He) = 6 ± 6(stat) ± 7(syst) eV; ϵ2p( 4 He) = +5 ± 3(stat) ± 4(syst) eV and Γ2p( 4 He) = 14 ±8(stat) ±5(syst) eV. These values are important for the constraints of the low-energy ¯ KN interaction in theoretical approaches.

Investigation of the structure of the few body kaonic nuclei using the method of hyperspherical functions in momentum space

The kaonic clusters KNN and KNNN are studied within the method of hyperspherical functions in the momentum representation. Binding energies and widths of three- and four-body nuclear quasibound states are calculated by employing realistic NN potentials and the energy dependent chiral KN interaction, as well as a phenomenological KN potential. The comparison of the results of calculations obtained in the framework of the variational method, Faddeev, Faddeev-Yakubovsky equations, and method of hyperspherical functions in configuration space are discussed.

Baryon–Baryon and Meson–Baryon Potentials with QCD-Based Short-Range Cores

A unified potential model of baryon–baryon and meson–baryon interactions at low energies is proposed. In this model, the short-range cores which simulate recent lattice QCD calculations are introduced. In baryon–baryon sector, our potentials give a very good agreement with NN and YN scattering data and have very similar behavior to those from the lattice QCD calculations. The πN and KN interactions are also well described in our model.

KK̄N and K̄K̄N Molecular States with I = 1/2, 3/2 and JP = 1/2+ Studied with Three-Body Faddeev Calculations

Using the Akaishi—Yannazaki (AY) and Hyodo—Weise (HW) effective KK̄, K̄N, K̄K̄ and KN interactions, we study possible existence of KK̄N and K̄K̄N molecule states with I = 1/2,3/2 and JP = 1/2+ by means of three-body Faddeev equations. We find that for HW potential, KK̄N and K̄K̄N systems with I = 1/2 both are bound hadron molecular states with about 10 MeV binding energy. The relativistic effects of kinetic energy are of the order of 4–5 MeV. AY potential would give larger binding energy because of overestimating K̄N interaction strength. Although there are attractive interactions in the case of I = 3/2, the interaction is too weak to bind the systems.

K N Potential and Θ+ in Lattice QCD

We study the s-wave KN interactions in the isospin I = 0, 1 channels and associated exotic state Theta+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to mpi = 871 MeV. The s-wave KN potentials are obtaine d from the Bethe-Salpeter amplitudes. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I = 1 potential. The I = 0 potential is found to have attractive well at mid range. The KN scattering phase shift s are calculated and compared with the experimental data.

Kaon-Nucleon potential from lattice QCD

We study the KN interactions in the I(J^{\pi})=0(1/2^-) and 1(1/2^-) channels and associated exotic state \Theta^+ from 2+1 flavor full lattice QCD simulation for relatively heavy quark mass corresponding to m_{\pi}=871 MeV. The s-wave KN potentials are obtained from the Bethe-Salpeter wave function by using the method recently developed by HAL QCD (Hadrons to Atomic nuclei from Lattice QCD) Collaboration. Potentials in both channels reveal short range repulsions: Strength of the repulsion is stronger in the I=1 potential, which is consistent with the prediction of the Tomozawa-Weinberg term. The I=0 potential is found to have attractive well at mid range. From these potentials, the $KN$ scattering phase shifts are calculated and compared with the experimental data.

Variational calculations forK¯–few-nucleon systems

Deeply bound KNN, KNNN, and KNNNN states are discussed. The effective force exerted by the K meson on the nucleons is calculated with static nucleons. Next the binding energies are obtained by solving the Schroedinger equation or by variational calculations. The dominant attraction comes from the S-wave {lambda}(1405) and an additional contribution is due to {sigma}(1385). The latter state is formed at the nuclear peripheries and absorbs a sizable piece of the binding energy. It also generates new branches of quasibound states. The lowest binding energies based on a phenomenological KN input fall into the 40- to 80-MeV range for KNN, 90-150 MeV for KNNN, and 120-220 MeV for K{alpha} systems. The uncertainties are due to unknown KN interactions in the distant subthreshold energy region.

On the K + d interaction at low energies

The Kd reactions are considered in the impulse approximationwithNN final-state interactions (FSI) taken into account. Realistic parameters for the KN phase shifts are used. The “quasi-elastic” energy region, in which the elementary KN interaction is predominantly elastic, is considered. The theoretical predictions are compared with the data on the K+d → K+pn, K+d → K0pp, K+d → K+d, and K+d total cross sections. The NN FSI effect in the reaction K+d → K+pn has been found to be large. The predictions for the Kd cross sections are also given for slow kaons, produced from ϕ(1020) decays, as the functions of the isoscalar KN scattering length a0. These predictions can be used to extract the value of a0 from the data.

¯N interaction from meson-exchange and quark-gluon dynamics

We investigate the ¯N interaction at low energies using a meson exchange model supplemented with a short-distance contribution from one-gluon exchange. The model is developed in close analogy to the meson-exchange KN interaction of the Julich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (ρ , ω exchange and higher-order box diagrams involving ¯* N , ¯Δ , and ¯*Δ intermediate states. The short-range part is assumed to receive additional contributions from genuine quark-gluon processes. The predicted cross-sections for ¯N for excess energies up to 150MeV are of the same order of magnitude as those for KN but with average values of around 20mb, roughly a factor two larger than for the latter system. It is found that the ω -exchange plays a very important role. Its interference pattern with the ρ -exchange, which is basically fixed by the assumed SU(4) symmetry, clearly determines the qualitative features of the ¯N interaction --very similiar to what happens also for the KN system.

THE S- AND P-WAVE ATTRACTION IN BOUND KNN, KNNN STATES

The deeply bound KNN and KNNN states are discussed and variational estimates of the binding energies are given. The basic KN amplitudes involve the deep subthreshold energy region, which is not under direct control. Large uncertainties are due to the KN interaction range. The dominant attraction comes from the S -wave Λ(1405). In the KNNN systems, an additional strong contribution comes from the P -wave Σ(1385) resonance.

The Fundamental Kaonic Nuclear ClusterK-pp

We have studied the structure of K − pp comprehensively by solving this three-body system exactly in a variational method, starting from the Ansatz that the Λ(1405) resonance (≡ Λ ∗ )i s aK − p bound state. We have found that our original prediction for the presence of K − pp as a compact bound system with M = 2322 MeV/c 2 , BK =4 8 MeV andΓ =6 1 MeV remains unchanged by varying the ¯ KN and NN interactions widely as far as they reproduce Λ(1405). The structure of K − pp reveals a molecular feature, namely, the K − in Λ ∗ as an “atomic center” plays a key role in producing strong covalent bonding with the other proton. We have shown that the elementary process, p+p → K + +Λ ∗ +p, which occurs in a short impact parameter and with a large momentum transfer, leads to unusually large self-trapping of Λ ∗ by the participating proton, since the Λ ∗ -p system exists as a compact doorway state propagating to K − pp.

Dense \=K Nuclei and Their Excited States

We have investigated the excited states as well as the ground state of various K nuclei, based on the improved version of antisymmetrized molecular dynamics method with a phenomenological KN interaction. Our calculation shows that the ground state of K nuclei forms dense state; more than 4 ρ 0 (ρ 0 being normal density). The two excited states of 1 1 CK - , (J π , T) = (½ + , 0) and (½ + , 1), are also deeply bound below the Σπ-emission threshold. They are the same J π state but have quite different structures from each other; T = 0 state has a well-developed clustering structure, while T = 1 state has a shell-like structure.

Short-range repulsion and isospin dependence in the kaon-nucleon(KN)system

The short-range properties of the KN interaction are studied within the meson-exchange model of the Juelich group. Specifically, dynamical explanations for the phenomenological short-range repulsion, required in this model for achieving agreement with the empirical KN data, are explored. Evidence is found that contributions from the exchange of a heavy scalar-isovector meson (a_0(980)) as well as from genuine quark-gluon exchange processes are needed. Taking both mechanisms into account a satisfactory description of the KN phase shifts can be obtained without resorting to phenomenological pieces.

Partial wave contributions to the antikaon potential at finite momentum

The momentum dependence of the antikaon optical potential in nuclear matter is obtained from a microscopic and self-consistent calculation using the meson-exchange Jülich KN interaction. Two self-consistent schemes are discussed, which would lead to substantially different predictions for the width of K nuclear bound states. The effect of higher partial waves of the KN interaction, beyond the L=0 component, is studied and found to have moderate but nonnegligible effects on the K nuclear potential at zero momentum. At momenta as large as 500 MeV /c, relevant in the analysis of heavy-ion collisions, the higher partial partial waves modify the K optical potential by nearly a factor of two.