A Measurable Angular Distribution for ${\bar B} \to D^{*} \tau^- {\bar\nu}_\tau$ Decays

Abstract

At present, the measurements of $R_{D^{(*)}}$ and $R_{J/\psi}$ hint at new physics (NP) in $b \to c \tau^- {\bar\nu}$ decays. The angular distribution of ${\bar B} \to D^* (\to D \pi) \, \tau^{-} {\bar\nu}_\tau$ would be useful for getting information about the NP, but it cannot be measured. The reason is that the three-momentum ${\vec p}_\tau$ cannot be determined precisely since the decay products of the $\tau^-$ include an undetected $\nu_\tau$. In this paper, we construct a measurable angular distribution by considering the additional decay $\tau^- \to \pi^- \nu_\tau$. The full process is ${\bar B} \to D^* (\to D \pi') \, \tau^{-} (\to \pi^- \nu_\tau) {\bar\nu}_\tau$, which includes three final-state particles whose three-momenta can be measured: $D$, $\pi'$, $\pi^-$. 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 $\pi^-$ emitted in the $\tau$ decay: the forward-backward asymmetry of the $\pi^-$ and the CP-violating triple-product asymmetry.