Few Nucleon Systems From Expanding About the Unitarity Limit

Can one understand the structure of nuclei at the physical point by an expansion about the unitarity limit? When the $NN$ $S$-wave binding energies are zero, the $NN$ system has no scale. Still, the $3N$ system has one dimensionful quantity $\Lambda_*$, related to the breaking of scale invariance to a discrete scaling symmetry (Efimov effect). The scale is set by the triton binding energy. While qualitatively this has been known for a long time, one may speculate that Nuclear Physics resides then in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear interaction and thus to be described by ``pionless'' EFT; but dense enough that the $NN$ scattering lengths are perturbatively close to the unitarity limit. In this case, $\Lambda_*$ sets the \emph{only} low-energy scale of all observables. Without it, no scale exists, and all nuclei have zero or infinite binding energy in the unitarity limit. For $A\le 4$ nucleons, the spectrum is indeed described well in this simplified version: a converging, perturbative expansion around the unitarity limit, with controlled corrections in the inverse scattering lengths, the interaction ranges and isospin breaking. [1] S.~K{\"o}nig, H.~W.~Grie{\ss}hammer, H.-W.~Hammer, U.~van Kolck: arXiv:1607.04623 [nucl-th].