Loop Corrections and Naturalness in a Chiral Effective Field Theory

TL;DR

This paper applies loop expansion techniques to a chiral effective hadronic Lagrangian, separating short- and long-range effects, and demonstrates that coupling parameters remain natural at two-loop order in nuclear matter calculations.

Contribution

It introduces a method using Infrared Regularization to handle loop corrections in chiral effective theories, ensuring natural parameter values at finite density.

Findings

Short-range effects are absorbed into local parameters.

Long-range contributions are nonlocal and calculable.

Coupling parameters remain natural after fitting to nuclear matter data.

Abstract

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. Nonlinear isoscalar scalar $(\sigma)$ and vector $(\omega)$ meson interactions are included, which incorporate many-nucleon forces and nucleon substructure. Calculations are carried out at the two-loop level to illustrate these techniques at finite nuclear densities and to verify that the coupling parameters remain natural when fitted to the empirical properties of equilibrium nuclear matter. Contributions from the $\omega N$ tensor coupling are also discussed.