The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas
Theorists love nontrivial fixed points. In the Unitarity Limit, the NN 𝑆-wave binding energies are zero, the scattering lengths infinite, Physics is universal, i.e. insensitive to details of the interactions, and observables display richer symmetries, namely invariance under both scaling and Wigner’s combined SU(4) transformation of spin and isospin. In “Pionless” EFT, both are explicitly but weakly broken and hence perturbative in the Unitarity Window (phase shifts 45° ≲ δ(k) ≲ 135°, i.e. momenta k≈mπ). This Unitarity Expansion provides strong hints that Nuclear Physics resides indeed in a sweet spot: bound weakly enough to be insensitive to the details of the nuclear interaction; and therefore interacting strongly enough that the NN scattering lengths are perturbatively close to the Unitarity Limit. In this paradigm change, NN details are less important than NNN interactions to explain the complexity and patterns of the nuclear chart. This presentation is a digest of the first quantitative exploration of corrections to this picture when pions are included [1] (see there for a more comprehensive list of references). Since the pion mass and decay constant introduce dimensionful scales in the NN system, they explicitly break the symmetries of the Unitarity fixed point. In χEFT, these symmetries must therefore be hidden and instead be classified as emergent.