Hilbert Series and Operator Basis for NRQED and NRQCD/HQET

We use a Hilbert series to construct an operator basis in the $1\mathrm{/}m$ 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 $d\le 8$. Comparing to the current literature, our results for NRQED agree for $d\le 8$, but there are some discrepancies in NRQCD/HQET at $d=7$ and 8.