Three-loop corrections to the muon and heavy quark decay rates

Recently, $O({\alpha }^3)$ corrections to the muon decay rate and $O({\alpha }_s^3)$ to heavy quark decays have been determined by Fael, Sch"onwald, and Steinhauser. This is the first such perturbative improvement of these important quantities in more than two decades. We reveal and explain a symmetry pattern in these new corrections, and confirm the most technically difficult parts of their evaluation.