Effective Field Theory for Few-Nucleon Systems

TL;DR

This paper surveys effective field theories for few‑nucleon systems, contrasting a pionless EFT that yields nonperturbative two‑ and three‑body results with a pionful EFT that incorporates chiral symmetry and explicit pions. It details the renormalization structure, power counting, and the emergence of phenomena such as a three‑body limit cycle in the pionless theory and the challenges of renormalization in the pionful regime. Key results include model‑independent predictions for deuteron form factors, polarizabilities, and capture processes, as well as insights into three‑ and four‑nucleon forces, isospin violation, and the connection to lattice QCD. The outlook emphasizes extending EFT to larger nuclei, halo systems, and nuclear matter, and leveraging lattice QCD to constrain low‑energy constants and validate the EFT framework.

Abstract

We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact interactions allows a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out to high orders, leading to high precision. At higher energies, an EFT that includes pion fields justifies and extends the traditional framework of phenomenological potentials. The correct treatment of QCD symmetries ensures a connection with lattice QCD. Several tests and prospects of these EFTs are discussed.

Figures (18)

• Figure 1: Graphs contributing to the LO $NN$ scattering amplitude.
• Figure 2: $^3S_1$$NN$ phase shift (in degrees) as function of the center-of-mass momentum. The LO result is the dashed (purple) line, the N$^2$LO the dotted (red) line and N$^4$LO the thick (blue) solid curve. The dot-dashed line is the Nijmegen PSA. From Ref. seattle_pionless, courtesy of M. Savage.
• Figure 3: Cross section for $\gamma+d\rightarrow n+p$ as function of the photon energy at N$^4$LO, compared to data. From Ref. Rupak_BBN, courtesy of G. Rupak.
• Figure 4: LO graphs contributing to the dressed propagator of the dimeron (a) and to the particle/dimeron amplitude (b).
• Figure 5: $k \cot\delta$ for $nd$ scattering in the quartet $S$-wave channel as function of the energy. The dashed line is the LO and the full line the N$^2$LO result stooges_dependence. Points are from a PSA data_quartet_phaseshifts and a near-threshold measurement data_quartet. Figure courtesy of H.-W. Hammer.