[Paper Review] Recent developments and applications of the relativistic chiral nuclear force

Li-Sheng Geng, Jun-Xu Lu+3 more|arXiv (Cornell University)|Mar 2, 2026

Nuclear physics research studies0 citations

TL;DR

A review of relativistic (covariant) chiral nuclear forces, their construction up to NNLO, key advantages over nonrelativistic approaches, and applications to nuclear matter, finite nuclei, and hypernuclei.

ABSTRACT

The nuclear force is central to our understanding of complex nuclear phenomena and to the applications of nuclear techniques. The nonperturbative nature of the low-energy strong interaction and the color confinement have made an ab initio understanding of the nuclear force a challenge for almost a century since the pioneering work of Yukawa. Since 1990, chiral effective field theory (ChEFT) has become the de facto standard for describing nuclear interactions--most prior studies employed heavy-baryon chiral perturbation theory. Only recently, there have been successful attempts to construct a chiral nuclear force employing covariant baryon chiral perturbation theory. In this work, we review recent developments and applications of relativistic chiral nuclear forces. We first elaborate on the necessity of relativistic/covariant theories, then present the construction of the first high-precision relativistic chiral nuclear force up to next-to-next-to-leading order (NNLO), and discuss the ongoing progress in higher-order nucleon-nucleon (NN) and $nd$ scattering, as well as their applications in nuclear matter, finite nuclei, and hypernuclear systems. Finally, we summarize the achievements and outline the future outlook of this research field.

Motivation & Objective

• Motivate the need for a relativistic (covariant) chiral nuclear force in describing nuclear systems.
• Describe the covariant construction of the chiral nuclear force within the EOMS scheme.
• Illustrate the first high-precision relativistic NN force up to NNLO and its phase-shift fits.
• Discuss progress toward higher-order relativistic forces and three-body/4N extensions.
• Summarize applications to nuclear matter, finite nuclei, and hypernuclear systems and outline future prospects.

Proposed method

• Construct covariant chiral Lagrangians that satisfy chiral symmetry and Lorentz invariance.
• Adopt a covariant power counting scheme (EOMS) to restore power counting in the one-baryon system.
• Solve a covariant scattering equation with a relativistic propagator to obtain T-matrix elements.
• Build the NN kernel at NNLO including 19 LECs from contact, OPE, and TPE terms with isospin breaking.
• Regularize loop contributions via spectral-function regularization and analyze cutoff dependence.
• Compare relativistic results with nonrelativistic ChEFT and experimental phase shifts, highlighting convergence and renormalizability improvements.

Experimental results

Research questions

• RQ1 How does a covariant (relativistic) chiral nuclear force compare to nonrelativistic counterparts in phase-shift descriptions and convergence?
• RQ2 Can a high-precision relativistic NN force be constructed up to NNLO and describe data up to ~200 MeV laboratory energy?
• RQ3 What are the implications of relativistic approaches for nuclear matter saturation, finite nuclei, and hypernuclear systems?
• RQ4 Does the relativistic framework improve renormalizability, convergence, and naturalness of low-energy constants (LECs) compared to NR approaches?
• RQ5 What is the status and outlook for higher-order relativistic chiral forces and relativistic three-body dynamics?

Key findings

• The first high-precision relativistic NN force up to NNLO reproduces phase shifts well up to T_lab ≈ 200 MeV.
• Relativistic NN forces show faster convergence and better renormalizability than nonrelativistic counterparts in several partial waves.
• LO relativistic forces can capture key nuclear dynamics with only four LECs without invoking three-nucleon forces in some contexts.
• NLO relativistic results for symmetric nuclear matter saturate within empirical regions without explicit 3NFs, indicating a relativistic origin for saturation.
• Relativistic ChEFT applied to finite nuclei (e.g., 40Ca–120Sn) describes binding energies and charge radii with notable accuracy, competing with NR approaches.
• Hypernuclear studies show LO covariant YN forces align better with data than NR YN forces, and Lambda single-particle potentials agree reasonably with empirical trends.