$\bar{K}+N\to K+\Xi$ reaction and $S=-1$ hyperon resonances

Abstract

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 amplitude. 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.

Comments: 19 pages, REVTeX, 12 figures, revised version