The $bar{K} + N to K + Xi$ reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon $s$- and $u$-channel contributions as well as a phenomenological contact ampl
itude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the $Lambda(1890)$, $Sigma(2030)$, and $Sigma(2250)$. For the latter resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265 MeV. The $Sigma(2030)$ resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the $Sigma(2250)$ resonance that is introduced to describe a small bump structure observed in the total cross section of $K^- + p to K^+ + Xi^-$. The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in $K^- + p to K^+ + Xi^-$, where the $P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the target-recoil asymmetries of the $bar{K} + N to K + Xi$ reaction are also presented.
Various model-independent aspects of the $bar{K} N to K Xi$ reaction are investigated, starting from the determination of the most general structure of the reaction amplitude for $Xi$ baryons with $J^P=frac12^pm$ and $frac32^pm$ and the observables t
hat allow a complete determination of these amplitudes. Polarization observables are constructed in terms of spin-density matrix elements. Reflection symmetry about the reaction plane is exploited, in particular, to determine the parity of the produced $Xi$ in a model-independent way. In addition, extending the work of Biagi $mathrm{textit{et al. } [Z. Phys. C textbf{34}, 175 (1987)]}$, a way is presented of determining simultaneously the spin and parity of the ground state of $Xi$ baryon as well as those of the excited $Xi$ states.
Based on reflection symmetry in the reaction plane, it is shown that measuring the transverse spin-transfer coefficient $K_{yy}$ in the $bar{K}N to KXi$ reaction directly determines the parity of the produced cascade hyperon in a model-independent wa
y as $pi_Xi =K_{yy}$, where $pi_Xi =pm 1$ is the parity. This result based on Bohrs theorem provides a completely general, universal relationship that applies to the entire hyperon spectrum. A similar expression is obtained for the photoreaction $gamma N to K K Xi$ by measuring both the double-polarization observable $K_{yy}$ and the photon-beam asymmetry $Sigma$. Regarding the feasibility of such experiments, it is pointed out that the self-analyzing property of the $Xi$s can be invoked, thus requiring only a polarized nucleon target.
The $eta$-meson production in photon- and hadron-induced reactions, namely, $gamma p to p eta$, $pi^- p to n eta$, $pp to ppeta$, and $pn to pneta$, are investigated in a combined analysis in order to learn about the relevant production mechanisms an
d the possible role of nucleon resonances in these reactions. We consider the nucleonic, mesonic, and nucleon resonance currents constructed within an effective Lagrangian approach and compare the results with the available data for cross sections and spin asymmetries for these reactions. We found that the reaction $gamma p to p eta$ could be described well with the inclusion of the well-established $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, and $D_{13}(1700)$ resonances, in addition to the mesonic current. Consideration of other well-established resonances in the same mass region, including the spin-5/2 resonances, $D_{15}(1675)$ and $F_{15}(1680)$, does not further improve the results qualitatively. For the reaction $pi^- p to n eta$, the $P_{13}(1720)$ resonance is found to be important for reproducing the structure observed in the differential cross section data. Our model also improves the description of the reaction $NN to NNeta$ to a large extent compared to the earlier results by Nakayama textit{et al.} [Phys. Rev. C textbf{68}, 045201 (2003)]. For this reaction, we address two cases where either the $S_{11}(1535)$ or the $D_{13}$ dominates. Further improvement in the description of these reactions and the difficulty to uniquely determine the nucleon resonance parameters in the present type of analysis are discussed.
