A Measurable Angular Distribution for ${\bar B} \to D^{*} τ^- {\barν}_τ$ Decays (2005.03032v2)
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 $q2$ 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.