The Unitarity-Limit Expansion for Two Nucleons with Perturbative Pions: Digest and Ideas

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. 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 classified as emergent. This text focuses on the $\chi$EFT variant with Perturbative ("KSW") Pions at next-to-next-to leading order (N2LO). 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 N3LO. Included are also ideas about underlying mechanisms and LO results of $\chi$EFT with Nonperturbative Pions in the expansion about Unitarity.