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Recent developments and applications of the relativistic chiral nuclear force

Li-Sheng Geng, Jun-Xu Lu, Qing-Yu Zhai, Zhi-Wei Liu, Shihang Shen

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.

Recent developments and applications of the relativistic chiral nuclear force

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 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.
Paper Structure (6 sections, 3 equations, 5 figures)

This paper contains 6 sections, 3 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Why a relativistic chiral nuclear force
  3. How to construct a relativistic chiral nuclear force
  4. The first high-precision relativistic chiral nuclear force
  5. Progress in higher order relativistic chiral nuclear forces
  6. Progress in the development of relativistic three-body scattering equation

Figures (5)

  • Figure S1: Scattering phase shifts of the $J\leq 2$ partial waves provided by different nuclear forces. The red solid lines result from our NNLO relativistic chiral nuclear force, and the momentum cutoff is set at $\Lambda=0.9$ GeV. The blue dashed lines result from the NLO relativistic chiral nuclear force, and the momentum cutoff is set at $\Lambda=0.6$ GeV. The corresponding shaded intervals are the theoretical uncertainties at the 68$\%$ confidence level. For comparison, we also present the results of the relativistic leading order (black dotted line, momentum cutoff $\Lambda=0.6$ GeV) and two non-relativistic N$^3$LO chiral nuclear forces, namely NR-N$^3$LO-Idaho ($\Lambda=0.5$ GeV, green dot-dashed line) Entem:2003ftMachleidt:2011zz, and NR-N$^3$LO-EKM ($\Lambda=0.9$ fm, purple short dot-dashed line) Epelbaum:2014efaEpelbaum:2014sza. The black solid points are the Nijmegen partial-wave analysis results Stoks:1993tb. Taken from Ref. Lu:2021gsb.
  • Figure S2: Same as Figure \ref{['fig1']} but for peripheral partial waves with $J \leq 4$ and $L \leq 4$. Note that for these partial waves, the chiral results are pure predictions without any free LECs. Taken from Ref. Lu:2021gsb.
  • Figure S3: Phase shifts and mixing angle for the $J=3$ partial waves. The gray, blue, and magenta bands are the results from the relativistic TPE $NN$ interactions at NLO, N$^2$LO, and N$^3$LO, respectively, with a cutoff in the range $[0.5, 0.8]$ GeV. For comparison, the N$^3$LO non-relativistic results are shown with orange bands (the two $F$-waves from Ref. Entem:2014msa and the $G$-waves from Ref. Entem:2015xwa). The solid and open dots represent the data from the Nijmegen multi-energy neutron-proton (n-p) phase shift analysis Stoks:1993tb and the VPI/GWU single-energy n-p analysis SM99 Arndt:1994br, respectively. Taken from Ref. Lu:2025ubc.
  • Figure S4: Same as Figure \ref{['fig3']} but for the $J=4$ partial waves. The solid and open dots are the data from the Nijmegen multi-energy n-p phase shift analysis Stoks:1993tb and the GWU n-p analysis SP07 Arndt:2007qn. Taken from Ref. Lu:2025ubc.
  • Figure S5: Same as Figure \ref{['fig4']} but for the $J=5$ partial waves. Taken from Ref. Lu:2025ubc.