# Tau properties in $B\to D\tau\nu$ from visible final-state kinematics

## TL;DR

This paper develops methods to extract tau polarization and asymmetry observables from visible decay products in $B o D au
u$ decays, enabling detailed studies of tau properties despite incomplete momentum reconstruction.

## Contribution

It provides explicit relations between tau properties and decay kinematics, allowing simultaneous extraction of polarization and asymmetry from angular distributions in specific decay channels.

## Key findings

- Potential 10% statistical precision for tau polarization and asymmetry at Belle II with 50 ab$^{-1}$ data.
- Explicit formulas linking tau properties to charged particle angular distributions.
- Feasibility of measuring tau polarization observables without full momentum reconstruction.

## Abstract

In semi-leptonic $B$ decays with a tau lepton, features of the production process are imprinted on the tau helicity states. Since the tau momentum cannot be fully reconstructed experimentally, the available information on the tau properties is encoded in its visible decay products. Focusing on the process $B\to D\tau\nu$, we find explicit relations between the tau properties and the kinematics of the charged particles in the decays $\tau\to\pi\nu$, $\tau\to\rho\nu$, and $\tau\to\ell\nu\bar{\nu}$. In particular, we show that the perpendicular polarization, $P_\perp$, and the forward-backward asymmetry, $A_\tau$, of the tau lepton can simultaneously be extracted from an angular asymmetry of the charged particle against the $D$ meson. For the most sensitive decay channel, $\tau\to\pi\nu$, we expect a relative statistical precision of about $10\%$ for $P_\perp$ and $A_\tau$ in a measurement based on $50\,$ab$^{-1}$ of data at BELLE II.