Improved Actions for Nuclear Effective Field Theories

TL;DR

This work addresses leading-order instabilities in nuclear Short-Range/EFTs by introducing improved actions that embed a fake interaction range at LO and compensate its effects perturbatively at higher orders. By testing with $^4$He clusters and extending to heavier systems, it shows that a controlled LO with a single perturbative parameter $x$ can yield bound-state energies close to experimental values, e.g., $B^{(1)}(^6Li) = 31.6$ MeV, $B^{(1)}(^12C) = 97$ MeV, and $B^{(1)}(^16O) = 156$ MeV for $x=1$, within roughly 20% of experiment. The method preserves the EFT's renormalization structure and a fixed breakdown scale $M_{hi}$, illustrating a pathway to describe nuclei up to modest $A$ while respecting the scale separation and discrete-scale-invariance features near unitarity. Further work with more nuclei and higher orders is needed to assess convergence, quantify uncertainties, and determine the limits of validity for this improved-action strategy.

Abstract

Effective field theories have been successful in describing nuclei up to the alpha particle but face significant challenges for larger nuclei due to leading-order instabilities. These issues can be addressed with the introduction of a fake interaction range at leading order, whose effects are compensated for in perturbation theory at higher orders. The calculation of two-body phase shifts and ground-state energies for up to five $^4$He atoms in a theory with only contact interactions shows that, as long as it remains smaller or comparable to the experimental effective range, the fake range does not alter the convergence of the EFT expansion but is often beneficial at the lowest orders. I discuss the implications of this improved-action approach to the ground-state energies of nuclei such as $^6$Li, $^{12}$C, and $^{16}$O.