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

Abstract

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 be determined precisely since the decay products of the ${\tau }^{-}$ include an undetected ${\nu }_{\tau }$. Therefore, the angular distribution of this decay cannot be measured. In this work, we construct a {\it measurable} angular distribution by considering the subsequent decay ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$. The full cascade 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 Lorentz structures of the new physics (NP) effective operators and an unpolarized initial ${\Lambda }_b$ state, the five-fold differential angular distribution can be expressed in terms of ten angular observables ${\mathcal{K}}_i(q^2,E_{\pi })$. By integrating over some of the five kinematic parameters, we define a number of observables, such as the ${\Lambda }_c$ spin polarization $P_{{\Lambda }_c}(q^2)$ and the forward-backward asymmetry of ${\pi }^{-}$ meson $A_{FB}(q^2)$, both of which can be represented by the angular observables ${\hat{\mathcal{K}}}_i(q^2)$. We provide numerical results for the entire set of the angular observables ${\hat{\mathcal{K}}}_i(q^2)$ 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 $\bar{B}\to D^{(\ast )}{\tau }^{-}{\bar{\nu }}_{\tau }$ decays has obvious effects on the angular observables ${\hat{\mathcal{K}}}_i(q^2)$, except ${\hat{\mathcal{K}}}_{1ss}(q^2)$ and ${\hat{\mathcal{K}}}_{1cc}(q^2)$.

Comments: 36 pages, 2 figures, 5 tables, matches to the version published in JHEP