Power counting in chiral effective field theory and nuclear binding

Chiral effective field theory (χEFT), 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 χEFT 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 H3, He3,4, Li6, and O16 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 O16 is either unbound with respect to the four α-particle threshold, or deformed, or both. Similarly, we find that the Li6 ground-state resides above the α-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 χEFT lack necessary diagrams - such as three-nucleon forces - to realistically describe nuclei with mass number A>4.