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In $\Lambda_b^0 \to \Lambda_c^+ (\to \Lambda^0 \pi^+) \tau^- \bar{\nu}_\tau $decay, the solid angle of the final-state particle $\tau^-$ cannot bedetermined precisely since the decay products of the $\tau^-$ include anundetected $\nu_\tau$. Therefore, the angular distribution of this decay cannotbe measured. In this work, we construct a {\it measurable} angular distributionby considering the subsequent decay $\tau^- \to \pi^- \nu_\tau$. The fullcascade decay is $\Lambda_b^0 \to \Lambda_c^+ (\to \Lambda^0 \pi^+)\tau^- (\to\pi^- \nu_\tau)\bar{\nu}_\tau$. The three-momenta of the final-state particles$\Lambda^0$, $\pi^+$, and $\pi^-$ can be measured. Considering all Lorentzstructures of the new physics (NP) effective operators and an unpolarizedinitial $\Lambda_b$ state, the five-fold differential angular distribution canbe expressed in terms of ten angular observables ${\cal K}_i (q^2, E_\pi)$. Byintegrating over some of the five kinematic parameters, we define a number ofobservables, such as the $\Lambda_c$ spin polarization $P_{\Lambda_c}(q^2)$ andthe forward-backward asymmetry of $\pi^-$ meson $A_{FB}(q^2)$, both of whichcan be represented by the angular observables $\widehat{{\cal K}}_i (q^2)$. Weprovide numerical results for the entire set of the angular observables$\widehat{{\cal K}}_i (q^2)$ and $\widehat{{\cal K}}_i$ both within theStandard Model and in some NP scenarios, which are a variety of best-fitsolutions in seven different NP hypotheses. We find that the NP which canresolve the anomalies in $\bar{B} \to D^{(*)} \tau^- \bar{\nu}_\tau$ decays hasobvious effects on the angular observables $\widehat{{\cal K}}_i (q^2)$, except$\widehat{{\cal K}}_{1ss} (q^2)$ and $\widehat{{\cal K}}_{1cc} (q^2)$.

The measurable angular distribution of $\Lambda_b^0 \to \Lambda_c^+ (\to \Lambda^0 \pi^+)\tau^- (\to \pi^- \nu_\tau)\bar{\nu}_\tau$ decay