A measurable angular distribution for $$ \overline{B}\to {D}^{\ast }{\tau}^{-}{\overline{v}}_{\tau } $$ decays

Abstract At present, the measurements of $$ {R}_{D^{\left(\ast \right)}} $$ R D ∗ and RJ/ψ hint at new physics (NP) in $$ b\to c{\tau}^{-}\overline{v} $$ b → c τ − v ¯ decays. The angular distribution of $$ \overline{B}\to {D}^{\ast}\left(\to D\pi \right){\tau}^{-}{\overline{v}}_{\tau } $$ B ¯ → D ∗ → Dπ τ − v ¯ τ would be useful for getting information about the NP, but it cannot be measured. The reason is that the three-momentum $$ {\overrightarrow{p}}_{\tau } $$ p → τ cannot be determined precisely since the decay products of the τ− include an undetected ντ. In this paper, we construct a measurable angular distribution by considering the additional decay τ−→ π−ντ. The full process is $$ \overline{B}\to {D}^{\ast}\left(\to D{\pi}^{\prime}\right){\tau}^{-}\left(\to {\pi}^{-}{v}_{\tau}\right){\overline{v}}_{\tau } $$ B ¯ → D ∗ → D π ′ τ − → π − v τ v ¯ 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 asymmetries. 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 π− emitted in the τ decay: the forward-backward asymmetry of the π− and the CP-violating triple-product asymmetry.

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