Chiral effective field theory and nuclear forces (1105.2919v1)

Abstract: We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.

• The paper introduces chiral effective field theory as a systematic method for deriving nuclear forces through a momentum expansion.
• The paper demonstrates how hierarchical interactions, notably three-nucleon forces, enhance the accuracy of few-nucleon system predictions.
• The paper validates chiral potentials via numerical analyses, showcasing their advantages over traditional phenomenological models.

Summary of "Chiral Effective Field Theory and Nuclear Forces"

The paper "Chiral Effective Field Theory and Nuclear Forces" by R. Machleidt and D.R. Entem focuses on the development and implications of chiral effective field theory (EFT) in describing nuclear forces. This research integrates low-energy quantum chromodynamics (QCD) with effective field theory, primarily targeting the phenomenological understanding and theoretical predictions of nucleon-nucleon interactions and the role of three-nucleon forces.

Key Highlights

1. Chiral Effective Field Theory (Chiral EFT):
   • Chiral EFT is based on the symmetries of low-energy QCD, specifically chiral symmetry and its breaking. It treats nucleons and pions as effective degrees of freedom rather than quarks and gluons.
   • The EFT approach is characterized by a power counting scheme that systematically organizes interactions in terms of a momentum expansion, providing a path to calculate nuclear forces order by order.
2. Hierarchy of Nuclear Forces:
   • Within chiral EFT, nuclear forces are derived as a hierarchical set of interactions starting from two-nucleon forces (2NF), with three-nucleon (3NF) and four-nucleon forces (4NF) emerging naturally as the calculation order increases.
   • The leading order (LO) includes one-pion exchange and two leading contact terms. Higher orders introduce two-pion exchange (2PE), more contact terms, and 3NF and 4NF contributions.
3. The Role of Three-Nucleon Forces (3NF):
   • At NNLO, the first significant three-nucleon forces appear, comprising two-pion exchange and one-pion exchange interactions. These 3NFs are found to be crucial for accurately describing few-nucleon systems and certain nuclear reactions.
   • Theoretical discrepancies in physical observables, like the nucleon-deuteron scattering length, are better reconciled with the inclusion of these additional forces.
4. Numerical Results and Applications:
   • The authors discuss numerical results indicating the need for higher-order potentials (such as N$^3$LO) for achieving a high-precision description of empirical nucleon-nucleon scattering data.
   • Chiral potentials have been applied successfully in calculations of nuclear structure of light and medium-mass nuclei, providing improved predictions over traditional models.
5. Comparison with Conventional Potentials:
   • The chiral interactions demonstrate an ability to reproduce known nuclear phenomenology while offering a path toward calculations that are rooted in fundamental QCD, compared to meson-exchange models that rely heavily on phenomenological adjustments.
   • The paper also discusses the relation to and advantages over established high-precision phenomenological potentials like AV18.
6. Future Implications and Open Questions:
   • The research explores future directions, including a detailed understanding of isospin violations, the introduction of $\Delta$-isobar degrees of freedom, and challenges in non-perturbative renormalization.
   • Further calculations at higher orders, such as N$^4$LO, are suggested to adequately address remaining discrepancies and enhance the description of nuclear systems.

This work forms the foundation for a rigorous and systematic approach to analyzing nuclear interactions, establishing chiral EFT as a powerful tool that bridges phenomenological nuclear physics and QCD. The detailed treatment of theoretical concepts, systematic development of potentials, and significant numerical results underscore its practical and theoretical ramifications in nuclear physics research.