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

Abstract

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. We further provide Monte Carlo samples of the 5D rate of the neutrino-inclusive decays $B\to P\mu X_{\bar{\nu }}$.

Comments: 14 pages, 6 figures, 3 ancillary files; v2 (as published): Corrected error in d^5Gamma, updated all numerical results; summary unchanged