^{*}

^{†}

magwwo@gmail.com

barros.celso@ufsc.br

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In this work we study the low energy kaon-hyperon interaction, considering effective chiral Lagrangians that include kaons,

A subject that is very interesting and remains not very well studied is low energy hyperon interactions. Despite the fact that experimental data for many hyperon processes are not available (for example the

In the study of hypernuclei structure

Another system where hyperon interactions are required is in the study of hyperon stars. Since the proposal of the hypothesis that hyperons could be produced inside neutron stars at high densities, many models have been proposed, as for example in

In high energy physics also this kind of interaction is very important. When studying hyperon polarization, produced in proton-nucleus and nucleus-nucleus collisions

For these reasons, this work will be devoted to the study of the kaon-hyperon (

This paper will present the following content: in Sec.

In order to study

In this section we will present the basic formalism that will be used to study kaon-hyperon interactions (it is the same one worked out in the study pion-hyperon interactions

For example, in

Calculating the diagrams, considering the interactions described by the Lagrangians above for an arbitrary process, the scattering amplitudes may be written in the form

The scattering matrix for an isospin state is given by the expression

Calculating the amplitudes at the tree level, the results obtained will be real, and then violate the unitarity of the

The differential cross sections may be calculated using the previous results,

An important task to achieve is to determine the coupling constant for each resonance that will be considered. We will adopt the same procedure considered in

In the following sections we will apply this formalism in the study of the reactions of interest.

Since the

In Fig.

Diagrams for the

Particles considered in the

For the calculation of the contribution of particles with spin-1/2 (

Calculating the Feynman diagrams and comparing with Eq.

In a similar way, we adapted the interaction Lagrangian

Calculating the amplitude for the exchange of a spin-3/2

For the spin-3/2

For the last diagram, Fig.

The parameters considered in the

Parameters for the

The coupling constants

For higher mass particle exchanges we consider the fact that the scattering amplitudes are dominated by these resonances when the energies are close to their masses, and then the phase shifts have the approximate form of the Breit-Wigner expression

Breit-Wigner fit for the

In Figure

Total cross section and phase shifts of the

Observing the figure, we can note that the resonances, and especially the

The

Diagrams for the

The parameters considered are those given before,

Total cross section and phase shifts of the

In this case the interacting particles have isospins 1/2 and 1 (

The scattering amplitude has the general form

The contributing diagrams are shown in Fig.

Diagrams for the

Resonances of the

The resulting amplitudes for nucleons in the intermediate state [Fig.

Figure

For the spin-isospin-3/2

For the

Thus, to calculate the observables for each reaction we use

Parameters for the

To determine the coupling constants

Using the isospin formalism for the elastic and the charge exchange scattering, we can determine the amplitudes for the reactions (that we name

Total cross section and phase shifts of the

In this case, we will proceed in the same way as in the last section for the

Diagrams for the

The Lagrangians are very similar to the ones used to study the

In this case we have the following reactions:

For diagram

Total cross section and phase shifts of the

In this work the low energy

For the

In the study of high energy hyperon polarization, produced in proton-nucleus and in heavy ion collisions, if we consider the polarizations obtained in the final-state interactions, the processes studied in this work may have some effect in the final polarization of the

These reactions are also important in the determination of nucleon-hyperon and hyperon-hyperon potentials, as they are subprocesses of these interactions, and, as discussed before, these interactions have a fundamental importance in the structure of hypernuclei and in hyperon stars. For example, in the reactions

Examples of kaon exchange in the

The study of the

We have shown that the study presented in this work is very important for many physical systems of interest, and for this reason it must be continued and improved in future works.

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001.

Considering a process where

For the energy and the three-momentum of the intermediary particles we also have the relations