A Measurable Angular Distribution for ${\bar B} \to D^{*} τ^- {\barν}_τ$ Decays

At present, the measurements of $R_{D^{(*)}}$ and $R_{J/ψ}$ hint at new physics (NP) in $b \to c τ^- {\barν}$ decays. The angular distribution of ${\bar B} \to D^* (\to D π) \, τ^{-} {\barν}_τ$ would be useful for getting information about the NP, but it cannot be measured. The reason is that the three-momentum ${\vec p}_τ$ cannot be determined precisely since the decay products of the $τ^-$ include an undetected $ν_τ$. In this paper, we construct a measurable angular distribution by considering the additional decay $τ^- \to π^- ν_τ$. The full process is ${\bar B} \to D^* (\to D π') \, τ^{-} (\to π^- ν_τ) {\barν}_τ$, which includes three final-state particles whose three-momenta can be measured: $D$, $π'$, $π^-$. The magnitudes and relative phases of all the NP parameters can be extracted from a fit to this angular distribution. One can measure CP-violating angular asymmmetries. If one integrates over some of the five kinematic parameters parametrizing the angular distribution, one obtains (i) familiar observables such as the $q^2$ distribution and the $D^*$ polarization, and (ii) new observables associated with the $π^-$ emitted in the $τ$ decay: the forward-backward asymmetry of the $π^-$ and the CP-violating triple-product asymmetry.

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