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
$45^\circ \lesssim \delta(𝑘) \lesssim 135^\circ$ , i.e. momenta $𝑘 \approx 𝑚 \pi $). 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 $\chi EFT$, these symmetries must therefore be hidden
and instead be classified as emergent. This text focuses on the $\chi EFT$ variant with Perturbative
(“KSW”) Pions at next-to-next-to leading order ($N^2LO$). In the $^1S_0$ channel up to cm momenta
$\lesssim 300 MeV$, the results are clearly converged order-by-order and agree very well with phase shift
analyses. Apparent large discrepancies in the $^3 S_1 $channel even at 𝑘 ≈ 100 MeV are remedied by
taking only the central part of the pion’s $N^2LO$ contribution. In contradistinction to the tensor
part, it does not mix the different Wigner-SU(4) multiplets and hence is identical in $^1 S_0$ and $^3 S_1$ .
With this formulation, pionic effects are small in both channels even for 𝑘 $\gtrsim 𝑚_\pi$ , i.e. where both
Unitarity and pion effects are expected to be relevant. This leads to the Hypothesis that both scale
invariance and Wigner-SU(4) symmetry in the Unitarity Expansion show persistence, i.e. the
footprint of both combined dominates even for 𝑘 $\gtrsim 𝑚_\pi$ and is more relevant than chiral symmetry,
so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE is suppressed and does not enter
before N3 LO. Included are also ideas about underlying mechanisms and LO results of $\chi EFT$ with
Nonperturbative Pions in the expansion about Unitarity.