Relativistic self-energy in nuclear dynamics

It is a well-known fact that Dirac phenomenology of nuclear forces predicts the existence of large scalar and vector mean fields in matter. To analyze the relativistic self-energy in a model independent way, modern high-precision nucleon-nucleon (NN) potentials are mapped on a relativistic operator basis using projection techniques. Comparison of the various potentials at the level of covariant amplitudes produced remarkable agreement. It allows further calculation of the relativistic self-energy in nuclear matter in the Hartree-Fock approximation. Independent of the choice of the nucleon-nucleon interaction large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. In the framework of chiral effective field theory, these fields are dominantly generated by contact terms that occur at next-to-leading order in the chiral expansion. Consistent with Dirac phenomenology the corresponding low-energy constants that generate the large fields are closely connected to the spin-orbit interaction in NN scattering. The connection to quantum chromodynamics sum rules is discussed as well.