Two-loop corrections for nuclear matter in the Walecka model

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Abstract
Two-loop corrections for nuclear matter, including vacuum polarization, are calculated in the Walecka model to study the loop expansion as an approximation scheme for quantum hadrodynamics. Criteria for useful approximation schemes are discussed, and the concepts of strong and weak convergence are introduced. The two-loop corrections are evaluated first with one-loop parameters and mean fields and then by minimizing the total energy density with respect to the scalar field and refitting parameters to empirical nuclear matter saturation properties. The size and nature of the corrections indicate that the loop expansion is not convergent at two-loop order in either the strong or weak sense. Prospects for alternative approximation schemes are discussed.