Hilbert series and operator basis for NRQED and NRQCD/HQET

We use a Hilbert series to construct an operator basis in the 1/m expansion of a theory with a nonrelativistic heavy fermion in an electromagnetic (NRQED) or color gauge field (NRQCD/HQET). We present a list of effective operators with mass dimension d≤8. Comparing to the current literature, our results for NRQED agree for d≤8, but there are some discrepancies in NRQCD/HQET at d=7 and 8.