Abstract
In \( {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}{\overline{v}}_{\tau } \) decay, the solid angle of the final-state particle τ− cannot be determined precisely since the decay products of the τ− include an undetected ντ. Therefore, the angular distribution of this decay cannot be measured. In this work, we construct a measurable angular distribution by considering the subsequent decay τ− → π−ντ. The full cascade decay is \( {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}\left(\to {\pi}^{-}{v}_{\tau}\right){\overline{v}}_{\tau } \). The three-momenta of the final-state particles Λ0, π+, and π− can be measured. Considering all Lorentz structures of the new physics (NP) effective operators and an unpolarized initial Λb state, the five-fold differential angular distribution can be expressed in terms of ten angular observables \( {\mathcal{K}}_i\left({q}^2,{E}_{\pi}\right) \). By integrating over some of the five kinematic parameters, we define a number of observables, such as the Λc spin polarization \( {P}_{\Lambda_c}\left({q}^2\right) \) and the forward-backward asymmetry of π− meson AFB(q2), both of which can be represented by the angular observables \( {\hat{\mathcal{K}}}_i\left({q}^2\right) \). We provide numerical results for the entire set of the angular observables \( {\hat{\mathcal{K}}}_i\left({q}^2\right) \) and \( {\hat{\mathcal{K}}}_i \) both within the Standard Model and in some NP scenarios, which are a variety of best-fit solutions in seven different NP hypotheses. We find that the NP which can resolve the anomalies in \( \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{v}}_{\tau } \) decays has obvious effects on the angular observables \( {\hat{\mathcal{K}}}_i\left({q}^2\right) \), except \( {\hat{\mathcal{K}}}_{1 ss}\left({q}^2\right) \) and \( {\hat{\mathcal{K}}}_{1 cc}\left({q}^2\right) \).
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Hu, QY., Li, XQ., Yang, YD. et al. The measurable angular distribution of \( {\Lambda}_b^0\to {\Lambda}_c^{+}\left(\to {\Lambda}^0{\pi}^{+}\right){\tau}^{-}\left(\to {\pi}^{-}{v}_{\tau}\right){\overline{v}}_{\tau } \) decay. J. High Energ. Phys. 2021, 183 (2021). https://doi.org/10.1007/JHEP02(2021)183
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DOI: https://doi.org/10.1007/JHEP02(2021)183