Symmetries of the Nucleon–Nucleon S-Matrix and Effective Field Theory Expansions

Abstract

The s-wave nucleon-nucleon 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.

Weinberg’s Compositeness

“…instead of Equation ( 8). For very different reasons, this type of potential has recently been considered as an alternative LO for the two-nucleon system at physical [53] (also with explicit pions [54]) and unphysical [55] quark masses. Here, it is easy to see that it yields Equation (20) if…”

Weinberg's Compositeness

“…( 8). For very different reasons, this type of potential has recently been considered as an alternative LO for the two-nucleon system at physical [53] (also with explicit pions [54]) and unphysical [55] quark masses. Here, it is easy to see that it yields Eq.…”

On-shell approximation for the s-wave scattering theory

“…In the lowenergy limit, which corresponds to consider only s-wave contribution to the phase shift, these calculations are based on the writing of an effective action of which only the terms contributing to the desired low-momentum expansion are retained. This EFT procedure was previously used to study the nucleon-nucleon scattering problem [19][20][21][22][23]. It is important to stress that, in the three dimensional case, the nonuniversal EFT corrections of Refs.…”