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$Ξ^-$ hyperon and hypernuclear production in the $(K^-,K^+)$ reaction on nucleon and nuclei in a field theoretical model

We investigate the production of a cascade hyperon ($Ξ$) and bound $Ξ^-$ hypernuclei in the $(K^-,K^+)$ reaction on proton and nuclear targets, respectively, within a covariant effective Lagrangian model. The $K^+Ξ^-$ production vertex is described by excitation, propagation and decay of $Λ$ and $Σ$ resonance states in the initial collision of a $K^-$ meson with a free or bound proton in the incident channel. The parameters of the resonance vertices are taken from previous studies and SU(3) symmetry considerations. The model is able to provide a good description of the available data on total and differential cross sections for the $p(K^-, K^+)Ξ^-$ reaction. The same mechanism was used to describe the hypernuclear production reactions $^{12}$C$(K^-,K^+)^{12}{/!/!/!_{/Xi^-}}$Be and $^{28}$Si$(K^-,K^+)^{28}{/!/!/!_{Ξ^-}}$Mg, where $Ξ$ bound state spinors calculated within a phenomenological model have been employed. Both the elementary and hypernuclear production cross sections are dominated by the contributions from the $Λ$(1520) intermediate resonant state. The beam momentum dependence of the $0^\circ$ differential cross sections for the formation of the $Ξ$ hypernuclei is found to be remarkably different from what has been observed previously in the impulse approximation model calculations