Heavy-to-Light-Quark Decays with Two-Loop Accuracy

We present a determination of a new class of three-loop Feynman diagrams describing heavy-to-light transitions. We apply it to find the $\mathcal{O}({\alpha }_s^2)$ corrections to the top quark decay $t\to bW$ and to the distribution of lepton invariant mass in the semileptonic $b$ quark decay $b\to ul\nu$. We also confirm the previously determined total rate of that process as well as the $\mathcal{O}({\alpha }^2)$ corrections to the muon lifetime.