On two nucleons near unitarity with perturbative pions
We explore the impact of perturbative pions on the Unitarity Expansion in the two-nucleon S-waves of Chiral Effective Field Theory at next-to-next-to leading order (N 2 LO). Pion exchange explicitly breaks the nontrivial fixed point’s universality, i.e. invariance of S waves under both conformal and Wigner’s combined SU(4) spin–isospin transformations. On the other hand, Unitarity explicitly breaks chiral symmetry. The two seem incompatible in their respective exact-symmetry limits. χEFT with Perturbative Pions in the Unitarity Expansion resolves the apparent conflict in the Unitarity Window (phase shifts 45° ≲ δ(k) ≲ 135°), i.e. around momenta most relevant for low-energy nuclear systems. Its only LO scale is the scattering momentum; NLO adds only scattering length, effective range and non-iterated one-pion exchange (OPE); and N 2 LO only once-iterated OPE. Agreement in the 1 S 0 channel is very good.