Reparameterization Invariant Operator Basis for NRQED and HQET

TL;DR

This paper develops a Lorentz-invariant operator basis for NRQED and HQET using Hilbert-series methods, ensuring reparameterization invariance and extending to operators of order 1/M^4 with gauge interactions.

Contribution

It introduces a systematic way to construct a reparameterization invariant operator basis for heavy particle effective theories up to order 1/M^4.

Findings

Operator basis tabulated up to order 1/M^4

Reparameterization invariance connects effective theories to Lorentz invariance

Hilbert-series methods effectively enumerate operators

Abstract

We discuss how reparameterization invariance connects a rotationally-invariant heavy particle effective theory with a single fermion to a Lorentz-invariant theory. Using Hilbert-series methods, a Lorentz-invariant operator basis is tabulated, up to and including operators of order $1/M^4$, when the fermion couples to an external $U(1)$ or $SU(3)$ gauge interaction.