Perturbation theory for a systematic account of the bound-state motion

TL;DR

This paper develops a perturbation theory for the Lorentz boost operator in two-nucleon systems, enabling systematic inclusion of relativistic corrections in low-energy effective field theories.

Contribution

It introduces a novel perturbation theory for the Lorentz boost operator expressed via nucleon-nucleon potentials, filling a gap in low-energy effective field theory approaches.

Findings

Provides a systematic method for relativistic boost corrections

Expresses boost operator in terms of established NN potentials

Complements existing low-energy EFT frameworks

Abstract

We derive a perturbation theory (PT) for the Lorentz boost operator in the space of two-nucleon wave functions. The latter is expressed in terms of the nucleon-nucleon ($NN$) potentials, developed so far in great detail for their use in the $NN$ scattering studies. The PT is designed to take into account the boost relativistic corrections in a systematic way and, as such, it is the only missing part in the corresponding approaches developed up to now in the low-energy effective field theories.