The antikaon potential in nuclear matter at finite momentum

We study the antikaon potential at finite momentum for proton and neutron nuclear matter. Our approach is based on the momentum dependence of the real part of the total $K^-N$ scattering amplitude, which is fixed in free space by experimental data, using the dispersion relation approach. We decompose the contributions to the scattering amplitude from different processes and consider the $\Lambda$(1405) and $\Sigma$(1385) to be dissolved in nuclear matter at density $\rho_0$. Within this approach the $K^-$ potential is found to be attractive up to high kaon momenta. Our result is in line with the data on the antikaon potential evaluated from the analysis of kaonic atoms (low momenta), heavy-ion (interdmediate momenta) and proton-nucleus (high momenta) collisions.