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

TL;DR

This paper calculates the detailed decay rates of B mesons involving tau leptons decaying to muons, highlighting their impact on measurements of semileptonic B decays and proposing methods to extract relevant ratios from experimental data.

Contribution

It provides a fully-differential decay rate calculation for B to P tau decays with tau to muon, aiding in background estimation and analysis of semileptonic B decay ratios.

Findings

Decays with three neutrinos significantly affect experimental measurements.

Analytic expressions enable testing of current and future experimental analyses.

Monte Carlo samples of decay rates are provided for simulation purposes.

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 $B\to P\mu X_{\bar\nu}$.