The NRQED lagrangian at order 1/M^4

TL;DR

This paper develops the NRQED effective lagrangian up to order 1/M^4, addressing Lorentz invariance constraints, and applies it to nuclear and atomic physics phenomena.

Contribution

It provides a complete construction of the NRQED lagrangian at order 1/M^4 with Wilson coefficient constraints and extends the theory to include interactions with light fermions.

Findings

Derived Wilson coefficient constraints ensuring Lorentz invariance.

Applied NRQED to nuclear structure effects in atomic states.

Analyzed radiative corrections in lepton-nucleon scattering.

Abstract

The parity and time-reversal invariant effective lagrangian for a heavy fermion interacting with an abelian gauge field, i.e., NRQED, is constructed through order $1/M^4$. The implementation of Lorentz invariance in the effective theory becomes nontrivial at this order, and a complete solution for Wilson coefficient constraints is obtained. Matching conditions in the one-fermion sector are presented in terms of form factors and two-photon matrix elements of the nucleon. The extension of NRQED to describe interactions of the heavy fermion with a light fermion is introduced. Sample applications are discussed; these include the computation of nuclear structure effects in atomic bound states, the model-independent analysis of radiative corrections to low-energy lepton-nucleon scattering, and the study of static electromagnetic properties of nucleons.