Impact of leptonic $\tau$ decays on the distribution of $B \to P \mu\bar\nu$ decays

Understand

We calculate the fully-differential rate of the decays $B\to P\tau(\to \mu\bar\nu\nu)\bar\nu$ where $P = D,\pi$, which is a background to the semimuonic decays $B\to P\mu\bar\nu$.

• The decays with a $3\nu$ final state can have a sizeable impact on the experimental analyses of the ratios $R_D$ and $R_\pi$, depending on the event selection in the analysis.
• We outline a strategy which permits the extraction of $R_P \mathcal{B}(\tau \to \mu\bar\nu\nu)$ from the neutrino-inclusive rate.
• Our analytic results can also be used to test both existing and upcoming experimental analyses.