Symmetries of Nucleon-Nucleon Scattering

The $S$-matrix for low-energy nucleon-nucleon scattering shows many properties that are not transparent in the effective action. Parameterized by momenta, the $S$-matrix can be viewed as flowing inside a region bounded by unitarity constraints. At the corners of this region, the $S$-matrix is at a fixed point of the RG and furnishes a representation of the Klein four-group. At leading order in the effective range expansion, the path that the $S$-matrix traces out has an isometry corresponding to a conformal (M\"obius) transformation. It is found that the curvature of this trajectory is related to the entanglement power of the $S$-matrix, a state-independent measure of operator entanglement. This is a new, more geometrical, way to think about entanglement.