Hidden Spin-Isospin Exchange Symmetry

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, Nc. However this large-Nc symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call Λlarge-Nc. We show that the large-Nc derivation requires a momentum resolution scale of Λlarge-Nc∼500 MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of P30 and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.