KN Phase Shifts Research Articles

$\bar KN$ SCATTERING IN CHIRAL CONSTITUENT QUARK MODELS

The chiral SU(3) quark model and the extended chiral SU(3) quark model have proven to be quite successful in reproducing the binding energy of the deuteron, the nucleon–nucleon (NN) scattering phase shifts and the hyperon–nucleon (YN) cross-sections. In the chiral SU(3) quark model, the quark–quark interaction contains one-gluon exchange (OGE), confinement potential and boson exchanges stemming from scalar and pseudoscalar nonets. In the extended chiral SU(3) quark model, the OGE is nearly replaced by vector meson exchange. It was shown in our previous work that these two models give quite similar descriptions for the S, P, D, F wave KN phase shifts, which means that in the KN system the contribution of OGE can be replaced by that of vector meson exchange. In this paper, we use the same models, the same parameters and the same methods to study the [Formula: see text] system with the purpose to test the effects of OGE and vector meson exchange. The cross-sections for K-p scattering into K-p, K0n, π+Σ-, π-Σ+, π0Σ0 and π0Λ channels are dynamically calculated by solving the resonating group method equation. While some channels are well described in one or the other model, a good agreement between the theoretical cross-sections and the experimental data for all channels is not successfully obtained. The present work indicates that both OGE and vector meson exchange are necessary to be included in the quark–quark interactions if one tries to simultaneously describe the KN phase shifts and [Formula: see text] cross-sections using one set of parameters in a constituent quark model.

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.

S, P, D, F WAVE KN PHASE SHIFTS IN THE CHIRAL SU(3) QUARK MODEL

The S, P, D, F wave KN phase shifts have been studied in the chiral SU (3) quark model by solving a resonating group method equation. The numerical results of different partial waves are in agreement with the experimental data except for the cases of P13 and D15, which are less well described when the laboratory momentum of the kaon meson is greater than 400 MeV.

KN Phase Shifts in Chiral SU(3) Quark Model**The project supported in part by National Natural Science Foundation of China under Grant No. 90103020

The isospin and kaon-nucleon S and P partial waves phase shifts have been studied in the chiral SU(3) quark model by solving a resonating group method equation. When the parameters of the chiral fields are taken in a reasonable region, the numerical results of S-wave are in good agreement with the experimental data, and the P-wave phase shifts can also be explained qualitatively by the calculation of only central force considered.

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.

KN phase shifts in a constituent quark model

In a first step, the I=1 and I=0 kaon–nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid hamiltonian method. The results have been compared to the nonrelativistic ones. For each isospin channel the phase shifts obtained are not so far from the nonrelativistic results. Then, K-nucleon p, d, f, g-waves phase shifts have been calculated using a nonrelativistic kinematics.

S, P, D, F, G-waves KN phase shifts in a constituent quark model with a spin–orbit interaction

The I=1 and I=0 kaon–nucleon s, p, d, f, g-waves phase shifts have been calculated in a nonrelativistic quark potential model using the resonating group method (RGM). The interquark potential includes gluon exchanges with a spin–orbit interaction. This force has been determined to reproduce as well as possible the meson and baryon spectra. The same force is employed for the cluster and intercluster dynamics and the relative KN wave-function is calculated without any approximation. While some channels are correctly described, the theory is still unable to explain others.

Influence of a relativistic kinematics on s-wave KN phase shifts in a quark model

The I=1 and I=0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid Hamiltonian method. The results have been compared to the non relativistic ones. For each isospin channel the phase shifts obtained are not so far from the non relativistic results.

Kaon-nucleon scattering amplitudes and Z* enhancements from quark Born diagrams.

We derive closed form kaon-nucleon scattering amplitudes using the ``quark Born diagram" formalism, which describes the scattering as a single interaction (here the OGE spin-spin term) followed by quark line rearrangement. The low energy I=0 and I=1 S-wave KN phase shifts are in reasonably good agreement with experiment given conventional quark model parameters. For $k_{lab}> 0.7$ Gev however the I=1 elastic phase shift is larger than predicted by Gaussian wavefunctions, and we suggest possible reasons for this discrepancy. Equivalent low energy KN potentials for S-wave scattering are also derived. Finally we consider OGE forces in the related channels K$\Delta$, K$^*$N and K$^*\Delta$, and determine which have attractive interactions and might therefore exhibit strong threshold enhancements or ``Z$^*$-molecule" meson-baryon bound states. We find that the minimum-spin, minimum-isospin channels and two additional K$^*\Delta$ channels are most conducive to the formation of bound states. Related interesting topics for future experimental and theoretical studies of KN interactions are also discussed.

KN scattering in the cloudy bag model: s, p, and d waves.

s-, p-, and d-wave KN phase shifts are calculated with the cloudy bag model (CBM). The results are in qualitative agreement with phase-shift analysis, except in those partial waves where exotic resonances are claimed to exist. However it seems that it is possible to get good agreement for these waves by just modifying the CBM potential, without including explicitly exotic states.