Theoretical predictions for inclusive B→Xuτν¯ decay

Abstract

With the expected large increase in datasets, previously not measured decays will be studied at Belle II. We derive standard model predictions for the $B\ensuremath{\rightarrow}{X}_{u}\ensuremath{\tau}\overline{\ensuremath{\nu}}$ decay rate and distributions. The region in the lepton energy spectrum where higher-dimension operators in the local operator product expansion 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 $\ensuremath{\tau}$ 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 $\ensuremath{\tau}$ polarization.