Theoretical predictions for inclusive $B\to X_u τ\barν$ decay

With the expected large increase in data sets, previously not measured decays will be studied at Belle II. We derive standard model predictions for the $B\to X_u τ\barν$ decay rate and distributions. The region in the lepton energy spectrum where higher-dimension operators in the local OPE need to be resummed into the $b$-quark light-cone distribution function is a significantly greater fraction of the phase space than for massless leptons. The finite $τ$ mass has the novel effect of shifting and squeezing how the distribution function enters the lepton energy spectrum. We also derive new predictions for the $τ$ polarization.

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