Simplification of chiral nuclear forces near the unitarity limit

TL;DR

The work shows that the tensor component of chiral nuclear forces can be moderated near the unitarity and chiral limits, enabling a perturbative-pion interaction (PPI) framework with a simple LO contact structure and perturbative OPE. PPI achieves accurate NN phase shifts up to k ≈ 300 MeV through a promoted SD counterterm and controlled higher-order corrections, while preserving an emergent SU(4) Wigner symmetry and nearing the unitarity limit. The approach yields comparable light-nucleus results to Pionless EFT, including 3N and 4N forces at LO/NLO, and demonstrates a viable path to ab initio calculations with fewer fine-tuned details. These findings offer a rationale for the success of simple short-range nuclear forces and suggest PPI as a practical framework for larger nuclei and nuclear matter.

Abstract

Modern theory approaches for describing atomic nuclei often make use of on an effective theory that constructs the interaction between nucleons systematically based on Quantum Chromodynamics (QCD), exploiting constraints arising from the approximate chiral symmetry of QCD. The tensor nuclear force produced by one-pion exchange is an important feature that arises naturally in this framework. In this work we show that, however, the tensor force is suppressed by the large nucleon-nucleon scattering lengths in combination with the smallness of the pion mass. Based on this observation, we propose a new scheme for a chiral nuclear force that is able to describe $NN$ phase shifts up to the center-of-mass momenta $k \simeq 300$ MeV while treating pion exchange as a perturbation. Our much simplified leading-order force provides a microscopic explanation for the recent success of various short-range nuclear forces from the perspective of chiral effective field theory, and it shares with those approaches an approximate Wigner SU(4) symmetry, as well as the closeness to the unitarity limit (infinite nucleon-nucleon scattering lengths), as guiding principles. Compared to previous approaches to perturbative-pion interactions, our force also adjusts the ordering of short-range contact interactions, by means of which we overcome convergence problems of the expansion that were previously assumed to severely limit its usefulness. We demonstrate the performance of our approach with numerical calculations of $NN$ scattering up to fourth order, in addition to studies of $3N$ and $4N$ bound-state properties.

Figures (6)

• Figure 1: Selected subleading Feynman diagrams of $NN$ scattering. The solid (dashed) represents the nucleon (pion).
• Figure 2: ${{{}^{3}\!{S}_{1}}\text{-}{{}^{3}\!{D}_{1}}}$ phase shifts and mixing angles as a function of the center-of-mass momentum $k$ with cutoff value $\Lambda = 800$ MeV. The solid circles are the empirical phase shifts from the Nijmegen group NNonlineStoks:1993tb. The green dot-dashed, red dashed, and dark solid lines correspond to NLO, N$^2$LO, and N$^3$LO respectively. The shaded bands indicate uncertainties estimated as $\pm (k \alpha_\pi)^{n-n_0+1}$ relative to the central values at each order N$^n$LO, with $n_0$ the first non-vanishing order.
• Figure 3: Binding energy of $^4\text{He}$ as functions of $\Lambda$ with the Pionless, PPI, and MMW. For MMW, the dashes lines indicate fits of the form $B(\infty) + P(1/\Lambda)$, with $P$ a polynomial without constant term.
• Figure 4: The point charge radii of $\isotope[3]{H}$ (upper panel) and $\isotope[4]{He}$ (lower panel) at LO/NLO from the Pionless, PPI, and nonperturbative-pion (MMW) scheme. The experimental point charge radii (dotted lines) are determined by converting the charge radii from Ref. Angeli:2013xyz according to Ref. Friar:1975aa.
• Figure SM1: $NN$ phase shifts and mixing angles from the PPI power counting, as functions of the center-of-mass momentum $k$ with cutoff value $\Lambda = 800$ MeV. The green dot-dashed, red dashed and black solid correspond to NLO, N$^2$LO and N$^3$LO respectively. The solid circles are the empirical phase shifts from the Nijmegen group NNonlineStoks:1993tb.