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Abstract

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<delta(k)<135deg,$k\approx m_\pi$) 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 N2LO only once-iterated OPE. Agreement in the 1S0 channel is very good. Apparent large discrepancies in the 3S1 channel at k>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.