Near-threshold $\eta^\prime$ meson production in ${\pi^-}A$ reactions

We study the inclusive near-threshold production of $\eta^\prime$ mesons in $\pi^-$ meson-nucleus reactions on the basis of the first-collision model relying on the nuclear spectral function and including incoherent processes of $\eta^\prime$ production in $\pi^-$ meson--proton collisions. The model accounts for the absorption of initial $\pi^-$ and final $\eta^\prime$ mesons, the binding of intranuclear protons and their Fermi motion, as well as the effect of the scalar $\eta^\prime$--nucleus potential (or the in-medium shift of the $\eta^\prime$ meson mass) on these processes. We calculate the differential and total cross sections for $\eta^\prime$ production off carbon and tungsten nuclei at laboratory angles of 0$^{\circ}$--10$^{\circ}$ and 10$^{\circ}$--45$^{\circ}$ by $\pi^-$ mesons with momentum of 1.7 GeV/c, which is close to the threshold momentum for $\eta^\prime$ creation on a free target proton at rest. We show that the calculated $\eta^\prime$ production cross sections are larger than those, studied earlier in the $\eta^\prime$ photoproduction reactions, by about two orders of magnitude. We also demonstrate that the high absolute values of the present differential and total $\eta^\prime$ production cross sections in the momentum ranges of 0.2--0.3 GeV/c and 0.1--0.6 GeV/c, respectively, possess a high sensitivity to changes in the in-medium shift of the $\eta^\prime$ mass. This offers the possibility of evaluating the above shift at these momenta from the respective data, which could be taken in future experiments at the GSI pion beam facility or at J-PARC.