Three-loop soft function for heavy-to-light quark decays

We compute the 1-jettiness soft function for the decay of a heavy quark into a light quark jet plus colorless particles at three-loop order in soft-collinear effective theory. The 1-jettiness measurement fixes the total small light-cone momentum component of the soft radiation with respect to the jet direction. This soft function is a universal ingredient to the factorization of heavy-to-light quark decays in the limit of small 1-jettiness. Our three-loop result is required for resummation at the N3LL′ level, e.g. near the endpoint in the photon energy spectrum of the B → Xsγ decay. It is also a necessary ingredient for future calculations of fully-differential heavy-to-light quark decay rates at N3LO using the N -jettiness subtraction method, e.g. for semileptonic top decays. Using our result for the soft anomalous dimension we confirm predictions on the universal infrared structure of QCD scattering amplitudes with a massive external quark at three loops.