Symmetries of the nucleon-nucleon S-matrix and effective field theory expansions

The s-wave nucleon-nucleon (NN) scattering matrix
(S-matrix) exhibits UV/IR symmetries which are hidden in the
effective field theory (EFT) action and scattering amplitudes, and
which explain some interesting generic features of the phase
shifts. These symmetries offer clarifying interpretations of
existing pionless EFT expansions, and suggest starting points for
novel expansions. The leading-order (LO) S-matrix obtained in the
pionless EFT with scattering lengths treated exactly is shown to
have a UV/IR symmetry which leaves the sum of s-wave phase shifts
invariant. A new scheme, which treats effective range corrections
exactly, and which possesses a distinct UV/IR symmetry at LO, is
developed up to NLO (next-to-LO) and compared with data.