Matching coefficients in NRQCD to two-loop accuracy

We consider the Lagrange density of non-relativistic Quantum Chromodynamics expanded up to order $1\mathrm{/}{m}^2$, where $m$ is the heavy quark mass, and compute several matching coefficients up to two-loop order. Our results are building blocks for next-to-next-to-next-to-leading logarithmic and next-to-next-to-next-to-next-to-leading order corrections to the threshold production of top quark pairs and the decay of heavy quarkonia. We describe the techniques used for the calculation and provide analytic results for a general covariant gauge.