Two-loop Corrections for Nuclear Matter in a Covariant Effective Field Theory

TL;DR

This paper develops a systematic approach to include two-loop corrections in covariant effective field theories for nuclear matter, ensuring natural parameter sizes and improved predictions of nuclear properties.

Contribution

It introduces a method using Infrared Regularization for two-loop calculations in a chiral effective hadronic Lagrangian, enhancing the theoretical framework for nuclear matter.

Findings

Two-loop corrections can be systematically included without destroying parameter naturalness.

Short-range effects are absorbed into local parameters, simplifying calculations.

The approach maintains consistency with empirical nuclear matter properties.

Abstract

Although one-loop calculations provide a realistic description of bulk and single-particle nuclear properties, it is necessary to examine loop corrections to develop a systematic finite-density power-counting scheme for the nuclear many-body problem when loops are included. Moreover, it is imperative to study exchange and correlation corrections systematically to make reliable predictions for other nuclear observables. One must also verify that the natural sizes of the one-loop parameters are not destroyed by explicit inclusion of many-body corrections. The loop expansion is applied to a chiral effective hadronic lagrangian; with the techniques of Infrared Regularization, it is possible to separate out the short-range contributions and to write them as local products of fields that are already present in our lagrangian. (The appropriate field variables must be re-defined at each order in loops.) The corresponding parameters implicitly include short-range effects to all orders in the interaction, so these effects need not be calculated explicitly. The remaining (long-range) contributions that must be calculated are nonlocal and resemble those in conventional nuclear-structure calculations. Calculations at the two-loop level are carried out to illustrate these techniques at finite densities and to verify that the coupling parameters remain natural when fitted to the empirical properties of equilibrium nuclear matter.