Exploring the $\tau$ polarization in $B\to X\tau\bar\nu$ along different axes

TL;DR

This paper investigates the tau polarization in inclusive B decays, aligning the theoretical framework with experimental measurements, and establishes a sum rule linking inclusive and exclusive decay polarizations to enhance new physics searches.

Contribution

It provides a consistent calculation of tau polarization in inclusive B decays using the same axis as exclusive decays and derives a sum rule connecting their polarizations.

Findings

Derived a sum rule relating inclusive and exclusive tau polarizations.

Predicted polarization for excited channels using experimental data and theoretical models.

Aligned polarization definitions to facilitate comparison between inclusive and exclusive decay analyses.

Abstract

The $\tau$ polarization in semileptonic $B$ decays provides probes of new physics complementary to decay rate distributions of the three-body final state. Prior calculations for inclusive decays used a definition for the polarization axis that is different from the choice used in calculations (and the only measurement) for exclusive channels. To compare inclusive and exclusive predictions, we calculate the $\tau$ polarization in inclusive $B\to X\tau\bar\nu$ using the same choice as in the exclusive decays, and construct a sum rule relating the inclusive $\tau$ polarization to a weighted sum of exclusive decay polarizations. We use this relation, experimental data, and theoretical predictions for the decays to the lightest charm or up-type hadrons to make predictions for excited channels.