Power counting in chiral effective field theory and nuclear binding

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 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 H-3, He-3,He-4, Li-6, and O-16 using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order, 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 <= 4. We find, however, that O-16 is either unbound with respect to the four alpha-particle threshold, or deformed, or both. Similarly, we find that the Li-6 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.