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. Pion exchange explicitly breaks the nontrivial fixed point's universality and invariance under conformal and Wigner-$\SU(4)$ spin-isospin transformations. This Chiral Effective Field Theory applies tothe Unitarity Window (45deg 100MeV are remedied by taking only the central part of the pion's N2LO contribution. In contradistinction to the tensor part, it is invariant under Wigner-SU(4)symmetry and hence identical in 1S0 and 3S1. NLO pions are Wigner-invariant. Both channels describe PWAs and pole parameters well within mutually consistent quantitative theory uncertainty estimates. Pionic effects are small, even for k>mpi. Empirically determined breakdown scales agree well with $\Lambda_{NN}=\frac{16\pi f_\pi^2}{g_A^2M}=300\;$MeV where iterated OPE is not suppressed. We therefore conjecture: The footprint of both scale invariance and Wigner-symmetry in the Unitarity Expansion shows persistence,i.e. both dominate even for k=mpi and are more relevant than chiral symmetry,so that the tensor/Wigner-SU(4) symmetry-breaking part of OPE does not enter before N3LO. We also discuss the potential relevance of entanglement power and possible resolution of a conflict with the strength of the tensor interaction in the large-Nc expansion.