Toward Chiral Theory of NN interactions in nuclear matter

The effective chiral theory of the in-medium NN interactions is considered. The shallow bound states, which complicate the effective field theory analysis in vacuum do not exist in matter. We show that the next-to-leading order terms in the chiral expansion of the effective Lagrangian can be interpreted as corrections so that the expansion is systematic. The Low Energy Effective Constants of this Lagrangian are found to satisfy the concept of naturalness. The potential energy per particle is calculated. The problems and challenges in constructing the chiral theory of nuclear matter are outlined.