Two-nucleon electromagnetic charge operator in chiral effective field theory (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>χ</mml:mi></mml:math>EFT) up to one loop

Abstract

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\ensuremath{\chi}$EFT) up to order $e\phantom{\rule{0.16em}{0ex}}Q$ [or next-to-next-to-next-to-next-to-leading order (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 nonstatic 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 nonuniqueness associated with these off-the-energy-shell effects.