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

TL;DR

This paper models the production of $\\Xi^-$ hyperons and hypernuclei in the $(K^-,K^+)$ reaction using a covariant effective Lagrangian, successfully describing experimental data and revealing new momentum dependence features.

Contribution

It introduces a covariant effective Lagrangian model for hyperon and hypernuclear production, incorporating resonance states and SU(3) symmetry, providing improved predictions over previous approaches.

Findings

Model accurately describes total and differential cross sections.

Hypernuclear production dominated by $\\Lambda$(1520) resonance.

Distinct beam momentum dependence observed compared to impulse approximation.

Abstract

We investigate the production of a cascade hyperon ($\Xi$) and bound $\Xi^-$ hypernuclei in the $(K^-,K^+)$ reaction on proton and nuclear targets, respectively, within a covariant effective Lagrangian model. The $K^+\Xi^-$ production vertex is described by excitation, propagation and decay of $\Lambda$ and $\Sigma$ 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 $p(K^-, K^+)\Xi^-$ reaction. The same mechanism was used to describe the hypernuclear production reactions $^{12}$C$(K^-,K^+)^{12}{/!/!/!_{/Xi^-}}$Be and $^{28}$Si$(K^-,K^+)^{28}{/!/!/!_{\Xi^-}}$Mg, where $\Xi$ 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 $\Lambda$(1520) intermediate resonant state. The beam momentum dependence of the $0^\circ$ differential cross sections for the formation of the $\Xi$ hypernuclei is found to be remarkably different from what has been observed previously in the impulse approximation model calculations