The two-nucleon electromagnetic charge operator in chiral effective field theory ($\chi$EFT) up to one loop

TL;DR

This paper derives the two-nucleon electromagnetic charge operator in chiral effective field theory up to one loop, clarifying the impact of off-the-energy-shell prescriptions on the operator's form and physical predictions.

Contribution

It provides a consistent derivation of the charge operator up to N4LO in $ ext{χ}$EFT, demonstrating the unitary equivalence of different off-shell prescriptions.

Findings

Different off-shell prescriptions lead to unitarily equivalent potentials and operators.

Predictions for physical observables are unaffected by off-shell ambiguities when a consistent set is used.

The derivation includes one-pion and two-pion exchange corrections up to N4LO.

Abstract

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\chi$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, predictions for physical observables will remain unaffected by the non-uniqueness associated with these off-the-energy-shell effects.