Medium effects in antikaon-induced Ξ− hyperon production on nuclei near threshold

We study the antikaon-induced inclusive cascade ${\Xi }^{-}$ hyperon production from ¹²C and ¹⁸⁴W target nuclei near threshold within a nuclear spectral function approach. The approach describes incoherent direct ${\Xi }^{-}$ hyperon production in elementary $K^{-}p\to K^{+}{\Xi }^{-}$ and $K^{-}n\to K^0{\Xi }^{-}$ processes as well as takes into account the influence of the scalar nuclear $K^{-}$, $K^{+}$, $K^0$, ${\Xi }^{-}$ and their Coulomb potentials on these processes. We calculate the absolute differential and total cross sections for the production of ${\Xi }^{-}$ hyperons off these nuclei at laboratory angles ≤ 45^∘ by $K^{-}$ mesons with momenta of 1.0 and 1.3 GeV/c, which are close to the threshold momentum (1.05 GeV/c) for ${\Xi }^{-}$ hyperon production on the free target nucleon at rest. We also calculate the momentum dependence of the transparency ratio for the ¹⁸⁴W/¹²C combination for ${\Xi }^{-}$ hyperons at these $K^{-}$ beam momenta. We show that the ${\Xi }^{-}$ differential and total (absolute and relative) production cross sections at the considered initial momenta reveal a distinct sensitivity to the variations in the scalar ${\Xi }^{-}$ nuclear potential at saturation density ${\rho }_0$, studied in the paper, in the low-momentum region of 0.1–0.6 GeV/c. We also demonstrate that for the subthreshold $K^{-}$ meson momentum of 1.0 GeV/c there is, contrary to the case of its above threshold momentum of 1.3 GeV/c, a strong sensitivity of the transparency ratio for ${\Xi }^{-}$ hyperons to the considered changes in the ${\Xi }^{-}$ nuclear potential at all outgoing ${\Xi }^{-}$ momenta as well, which cannot be masked, as in the case of differential and total observables mentioned above, by that associated with the possible changes in the poorly known experimentally ${\Xi }^{-}N$ inelastic cross section. Therefore, the measurement of these absolute and relative observables in a dedicated experiment at the J-PARC Hadron Experimental Facility will provide valuable information on the ${\Xi }^{-}$ in-medium properties, which will be complementary to that deduced from the study of the inclusive ($K^{-}$,$K^{+}$) reactions at incident momenta of 1.6–1.8 GeV/c in the ${\Xi }^{-}$ bound and quasi-free regions.