Power counting in chiral effective field theory and nuclear binding

TL;DR

This paper systematically studies RG-invariant chiral effective field theory formulations for nuclear binding, revealing limitations in current schemes for nuclei with mass number greater than 4, and highlighting the need for additional interactions.

Contribution

It provides the first systematic analysis of RG-invariant $ ext{chi}$EFT formulations for nuclear binding energies up to $A=16$, identifying their successes and shortcomings.

Findings

RG-invariant $ ext{chi}$EFT can predict nuclei with $A \,\leq 4$ accurately.

Predictions for $^{16}$O and $^{6}$Li deviate from experimental data.

Current schemes at LO lack necessary diagrams like three-nucleon forces.

Abstract

Chiral effective field theory ($\chi$EFT), as originally proposed by Weinberg, promises a theoretical connection between low-energy nuclear interactions and quantum chromodynamics (QCD). However, the important property of renormalization-group (RG) invariance is not fulfilled in current implementations and its consequences for predicting atomic nuclei beyond two- and three-nucleon systems has remained unknown. In this work we present a first and systematic study of recent RG-invariant formulations of $\chi$EFT and their predictions for the binding energies and other observables of selected nuclear systems with mass-numbers up to $A =16$. Specifically, we have carried out ab initio no-core shell-model and coupled cluster calculations of the ground-state energy of $^3$H, $^{3,4}$He, $^{6}$Li, and $^{16}$O using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order (NLO), where the subleading interactions are treated in perturbation theory. Our calculations indicate that RG-invariant and realistic predictions can be obtained for nuclei with mass number $A \leq 4$. We find, however, that $^{16}$O is either unbound with respect to the four $\alpha$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}$Li ground-state resides above the $\alpha$-deuteron separation threshold. These results are in stark contrast with experimental data and point to either necessary fine-tuning of all relevant counterterms, or that current state-of-the-art RG-invariant PC schemes at LO in $\chi$EFT lack necessary diagrams -- such as three-nucleon forces -- to realistically describe nuclei with mass number $A>4$.