Theoretical predictions for inclusive $B\to X_u \tau \bar\nu$ decay

TL;DR

This paper provides theoretical predictions for the inclusive B to X_u tau nu decay, including decay rates, distributions, and tau polarization, accounting for the tau mass effects, to aid upcoming experimental measurements at Belle II.

Contribution

It introduces the first detailed standard model predictions for B to X_u tau nu decays, incorporating finite tau mass effects and the impact on the lepton energy spectrum and polarization.

Findings

The lepton energy spectrum region requiring resummation is larger for tau leptons.

Finite tau mass shifts and squeezes the distribution function's influence.

New predictions for tau polarization in B decays.

Abstract

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 $B\to X_u \tau\bar\nu$ 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 $\tau$ 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 $\tau$ polarization.