The $\overline{K}N\to K\mathrm{\Xi }$ reaction in coupled-channels chiral models up to next-to-leading order

The meson-baryon interaction in $s$ wave in the strangeness $S=-1$ sector has been studied, employing a chiral SU(3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The parameters of the Lagrangian have been fitted to a large set of experimental data in different two-body channels, paying special attention to the $\overline{K}N\to K\mathrm{\Xi }$ reaction, which is particularly sensitive to the NLO terms. With the aim of improving the model in the $K\mathrm{\Xi }$ production channels, effects of the high spin hyperon resonances $\mathrm{\Sigma }\left(2030\right)$ and $\mathrm{\Sigma }\left(2250\right)$ have been taken into account phenomenologically.

Figure 1

Diagrammatic solution of the Bethe-Salpeter equation, where the interaction kernel $V$ is represented by the empty blobs, the scattering matrix $T$ by the solid blobs, and the loop function $G$ is represented by the intermediate baryon-meson propagators.

Figure 2

Total cross sections for the $K^{-}p\to K^{-}p,{\overline{K}}^{0}n,{\pi }^{-}{\mathrm{\Sigma }}^{+},{\pi }^{+}{\mathrm{\Sigma }}^{-},{\pi }^0{\mathrm{\Sigma }}^0,{\pi }^0\mathrm{\Lambda }$ reactions obtained from the WT (no $K\mathrm{\Xi }$) fit (dotted line), the NLO (no $K\mathrm{\Xi }$) fit (dashed line), the WT fit (dot-dashed line), and the NLO fit (solid line), where the last two cases take into account the experimental data of the $K\mathrm{\Xi }$ channels; see text for more details. Experimental data are from [42, 43, 44, 45]. The points in red have not been included in the fitting procedure.

Figure 3

The total cross sections of the $K^{-}p\to K^0{\mathrm{\Xi }}^0,K^{+}{\mathrm{\Xi }}^{-}$ reactions obtained from the WT (no $K\mathrm{\Xi }$) fit (dotted line), the NLO (no $K\mathrm{\Xi }$) fit (dashed line), the WT fit (dot-dashed line), and the NLO fit (solid line). Experimental data are from [46, 47, 48, 49, 50, 51, 52].

Figure 4

Total cross sections of the $K^{-}p\to K^{-}p,{\overline{K}}^{0}n,{\pi }^{-}{\mathrm{\Sigma }}^{+},{\pi }^{+}{\mathrm{\Sigma }}^{-},{\pi }^0{\mathrm{\Sigma }}^0,{\pi }^0\mathrm{\Lambda }$ reactions for the NLO* fit (dashed line), the WT+RES fit (dotted line), and the NLO+RES fit (solid line). Experimental data are from [42, 43, 44, 45]. The points in red have not been included in the fitting procedure.

Figure 5

Total cross sections of the $K^{-}p\to K^0{\mathrm{\Xi }}^0,K^{+}{\mathrm{\Xi }}^{-}$ reactions for the NLO* fit (dashed line), the WT+RES fit (dotted line), and the NLO+RES fit (solid line); see the text for more details. Experimental data are from [46, 47, 48, 49, 50, 51, 52].

Figure 6

Differential cross section of the $K^{-}p\to K^0{\mathrm{\Xi }}^0$ reaction for the NLO* fit (dashed line), the WT+RES fit (dotted line), and the NLO+RES fit (solid line); see the text for more details. Experimental data are from [46, 47, 48, 49, 50, 51, 52].

Figure 7

Differential cross section of the $K^{-}p\to K^{+}{\mathrm{\Xi }}^{-}$ reaction for the NLO* fit (dashed line), the WT+RES fit (dotted line), and the NLO+RES fit (solid line); see the text for more details. Experimental data are from [46, 47, 48, 49, 50, 51, 52].