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arXiv · 1911.04494

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

Robin Brüser·Ze Long Liu·Maximilian Stahlhofen
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Abstract

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 N$^3$LL$^\prime$ level, e.g. near the endpoint in the photon energy spectrum of the $B \to X_s \gamma$ decay. It is also a necessary ingredient for future calculations of fully-differential heavy-to-light quark decay rates at N$^3$LO 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.

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Robin Brüser, Ze Long Liu, Maximilian Stahlhofen. 2019-11-11. Three-loop soft function for heavy-to-light quark decays. https://doi.org/10.1007/jhep03(2020)071

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