Exploring the τ polarization in B→Xτν̄ along different axes

The 𝜏 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 𝜏 polarization in inclusive 𝐵→𝑋⁢𝜏⁢¯𝜈 using the same choice as in the exclusive decays, and construct a sum rule relating the inclusive 𝜏 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.