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

Abstract

At present, the measurements of $R_{D^{(\ast )}}$ and $R_{J/\psi }$ hint at new physics (NP) in $b\to c{\tau }^{-}\bar{\nu }$ decays. The angular distribution of $\bar{B}\to D^{\ast }(\to D\pi ){\tau }^{-}{\bar{\nu }}_{\tau }$ 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 $\bar{B}\to D^{\ast }(\to D{\pi }^{\prime }){\tau }^{-}(\to {\pi }^{-}{\nu }_{\tau }){\bar{\nu }}_{\tau }$, which includes three final-state particles whose three-momenta can be measured: $D$, ${\pi }^{\prime }$, ${\pi }^{-}$. 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 $D^{\ast }$ 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.

28 pages, 2 figures, 7 tables, presentation format for angular distribution revised, typos corrected, references added, to appear in JHEP

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