Nuclear and Few-Body EFT

Large scattering lengths and shallow bound states make nuclear physics an instructive effective-theory problem: some interactions must be summed even at low energy. This chapter chooses between pionless and chiral descriptions, then connects two- and three-body renormalization to currents and controlled uncertainties.

Enter this chapter

Begin with Chiral EFT for Pions and Nucleons to identify the pion and nucleon variables of a chiral expansion.

Topics

1. Chiral EFT for Pions and Nucleons — Introduces nucleons into the nonlinear chiral theory.
2. Nuclear Forces and the Chiral Expansion — Orders force kernels and identifies interactions needing iteration.
3. Pionless EFT and Shallow Two-Body Systems — Treats resonant two-body scattering below the pion scale.
4. Three-Body Renormalization and Universality — Determines when a new three-body input is required.
5. Electroweak Currents in Few-Body Systems — Matches currents consistently with nuclear states and forces.
6. Nuclear Predictions and Uncertainties Across Methods — Separates truncation, parameter, regulator, and numerical errors.

How the ideas fit together

A shallow pole makes repeated leading interactions as important as the first insertion. Iteration then exposes ultraviolet sensitivity that must be absorbed by counterterms at the same claimed order; in a resonant three-body channel, two-body data alone can be insufficient. The same consistency extends to external probes: changing the nuclear interaction without its associated currents need not preserve matrix elements. Regulator independence tests the assembled observable, not an isolated potential. Hammer, König, and van Kolck 2020, § II.

Where to go next

Continue to Electroweak Theory and the Higgs to specify the representations and hypercharges before deriving masses.

References

• Hammer, Hans-Werner, Sebastian König, and U. van Kolck. “Nuclear Effective Field Theory: Status and Perspectives.” Reviews of Modern Physics 92 (2020): 025004. DOI.