High-Precision Nuclear Forces From Chiral EFT: State-of-the-Art, Challenges, and Outlook

Abstract

Recently, a new generation of nuclear forces has been developed in the framework of chiral EFT. An important feature of these potentials is a novel semilocal regularization approach that combines the advantages of a local regulator for long-range interactions with the convenience of an angle-independent nonlocal regulator for contact interactions. The authors discuss the key features of the semi-local two-nucleon potentials and demonstrate their outstanding performance in the twonucleon sector by showing selected results up to fifth order in the EFT expansion. Also reviewed are applications to heavier systems, which are currently limited to third chiral order. This limitation reflects the conceptual difficulty in constructing a consistently regularized many-body forces and current operators and affects all currently available interactions. The authors outline possible ways to tackle this problem and discuss future directions in the field.

A Guided Tour of ab initio Nuclear Many-Body Theory

“…In chiral EFT with explicit nucleons and pions, = χ is traditionally considered to be in the range 700 − 1000 MeV, although newer analyses of observable truncation errors using Bayesian methods favor slightly lower values [34][35][36]. From a chiral EFT Lagrangian, one can then construct a systematic low-momentum expansion of nuclear interactions, as shown in Figure 2 (see references [2,3,32,37,39]). These interactions consist of (multi-)pion exchanges between nucleons, indicated by dashed lines, as well as nucleon contact interactions.…”

“…The different types of vertices are proportional to the low-energy constants (LECs) of chiral EFT, which encode physics that is not explicitly resolved because it involves either a high momentum scale or excluded degrees of freedom. Eventually, one hopes to calculate these LECs directly from the underlying QCD either through matching or renormalization group evolution of the couplings (see section 2.2), but at present, the LECs are fit to experimental data [3,4,[39][40][41].…”

“…As argued in sections 2.3.3 and 2.3.6, bases built on particlehole type expansions are not ideally suited to the description of collective correlations. The SA-NCSM [139] instead uses irreducible representations of SU (3) or Sp (3, ), the dynamical symmetry groups of collective models [263], to achieve a much more efficient description of collective behavior in nuclei. This is illustrated for the case of 20 Ne in Figure 14.…”

“…Over the past decade, the reach and capabilities of ab initio nuclear many-body theory have grown exponentially. The widespread adoption of Renormalization Group (RG) techniques, in particular the Similarity Renormalization Group (SRG) [1], and Effective Field Theory (EFT) [2][3][4] in the 2000s laid the foundation for these developments. Consistent two-nucleon (NN) and three-nucleon (3N) interactions from chiral EFT were quickly established as a new "standard" inputs for a variety of approaches, which made true multi-method benchmarks possible.…”

Self-Consistent Green's Function Theory for Atomic Nuclei

“…The third point implies that the EFT error can (and should) be subsequently propagated to many-body observables. This has been done in practice only very recently (see e.g., [16,[87][88][89][90][91][92]) and more formal and technical developments along these lines will be required in the future. Mainly three different χ-EFT Hamiltonians have been employed in recent GF calculations, all of which are discussed here.…”