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

TL;DR

This paper uncovers hidden UV/IR symmetries in the nucleon-nucleon S-matrix within effective field theory, explaining phase shift features and guiding new expansion schemes, with practical comparisons to data.

Contribution

It reveals UV/IR symmetries in the NN S-matrix and introduces a novel EFT expansion scheme that treats effective range corrections exactly.

Findings

LO S-matrix has a UV/IR symmetry preserving phase shift sums

New EFT scheme with exact effective range corrections shows improved agreement with data

Symmetries clarify features of pionless EFT expansions

Abstract

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 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.