The nucleon-nucleon interaction in a chiral effective field theory

We derive the nucleon-nucleon interaction based on the most general chiral effective pion-nucleon Lagrangian using the method of unitary transformations. For that, we develop a power counting scheme consistent with this projection formalism. In contrast to previous results obtained in old-fashioned time-ordered perturbation theory, the method employed leads to energy-independent potentials. We discuss in detail the similarities and differences to the existing chiral nucleon-nucleon potentials. We also show that to leading order in the power counting, the three-nucleon forces vanish lending credit to the result obtained by Weinberg using old-fashioned time-ordered perturbation theory. We employ the chiral nucleon-nucleon potential to study scattering and bound state problems in the two-nucleon system. At next-to-leading order, this potential is the sum of renormalized one-pion and two-pion exchange and contact interactions. At next-to-next-to-leading order, we have additional chiral two-pion exchange with low-energy constants determined from pion-nucleon scattering. Alternatively, we consider the delta-resonance as an explicit degree of freedom in the effective field theory. The nine parameters related to the contact interactions can be determined by a fit to the neutron-proton S- and P-waves and the mixing parameter ε1 for laboratory energies below 100 MeV. The predicted phase shifts and mixing parameters for higher energies and higher angular momenta are mostly well described for energies below 300 MeV. The S-waves are described as precisely as in modern phenomenological potentials. We observe a good agreement with experimentally measured deuteron properties. We also discuss various charge symmetry and charge independence breaking effects in the 1S0 channel, in which the largest isospin violating effects are observed. (orig.)