Power counting in chiral effective field theory and nuclear binding

Abstract

Chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$, 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 $\ensuremath{\chi}\mathrm{EFT}$ 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 $^{3}\mathrm{H}$, $^{3,4}\mathrm{He}$, $^{6}\mathrm{Li}$, and $^{16}\mathrm{O}$ 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 $A\ensuremath{\le}4$. We find, however, that $^{16}\mathrm{O}$ is either unbound with respect to the four $\ensuremath{\alpha}$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}\mathrm{Li}$ ground-state resides above the $\ensuremath{\alpha}$-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 $\ensuremath{\chi}\mathrm{EFT}$ lack necessary diagrams---such as three-nucleon forces---to realistically describe nuclei with mass number $A>4$.