Speaker
Description
Theorists love the unitarity limit: the $NN$ $S$-wave binding energies are zero, the scattering lengths infinite, and one has more symmetries. In "pionless" EFT, Efimov's $3N$ scale sets the only low-energy scale of all observables for a convergent, perturbative expansion around the unitarity limit. There are strong hints that Nuclear Physics resides indeed in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear interaction; but dense enough that the $NN$ scattering lengths are perturbatively close to the unitarity limit. In this paradigm change, details of two-nucleon interactions are less important than three-nucleon interactions to explain the complexity and patterns of the nuclear chart.
This presentation explores quantitatively the corrections to this picture when pions are included perturbatively. Their mass and decay constant provide dimensionful scales already in the $NN$ system, and thus explicitly break the unitarity symmetries. The "KSW" version of Chiral EFT has a well-defined power counting. Its leading order is identical to pionless EFT, so unitarity is broken "weakly''. Utilising the work by Fleming, Mehen and Stewart up to next-to-next-to-leading order, one finds that perturbative pions describe the $NN$ system well in the range in which pionless EFT applies as well. Beyond that, the series converges up to momenta of about $200\;$MeV in the $^1$S$_0$ channel, while the $^3$SD$_1$ channel appears to show strong fine-tuning. Consequences and possible remedies are discussed.
Work in collaboration with Y.-P. Teng (GW and U. of Wisconsin).
