Systematic calculation of s-wave pion and kaon self-energies in asymmetric nuclear matter

We calculate the pion self-energies in asymmetric nuclear matter in the two-loop approximation of chiral perturbation theory. We find three types of corrections beyond the well-known linear density approximation. The resulting s-wave potential (or equivalent mass-shift) of a π− in the center of a heavy nucleus like Pb turns out to be Uπ−=Δmπ−≃14 MeV, about half of what is needed to form the deeply bound and narrow pionic atom-states recently observed at GSI. The potential for a π+ under the same conditions is Uπ+=Δmπ+≃−1 MeV. In the same way we calculate the mass-shifts of K+-mesons in symmetric nuclear matter and neutron matter and find an increase of the K+-mass by 9% and 5%, respectively. As a further application we give an analytical result for the third order term in the scattering length expansion of the in-medium self-energy of an interacting light-boson/heavy-fermion system.