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

TL;DR

This paper develops a measurable angular distribution framework for the decay $oldsymbol{ ext{Lambda}_b^0 o ext{Lambda}_c^+ ( o ext{Lambda}^0 ext{pi}^+) au^- ( o ext{pi}^- u_ au)ar{ u}_ au$, accounting for undetected neutrinos, and explores its sensitivity to new physics scenarios.

Contribution

It constructs a five-fold differential angular distribution with ten observables for the cascade decay, including effects of new physics, and provides numerical predictions within the Standard Model and beyond.

Findings

Angular observables are sensitive to new physics effects.

Certain NP scenarios significantly alter specific angular observables.

Some observables remain unaffected by NP, aiding in model discrimination.

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 ${\cal K}_i (q^2, E_\pi)$. 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 $\widehat{{\cal K}}_i (q^2)$. We provide numerical results for the entire set of the angular observables $\widehat{{\cal K}}_i (q^2)$ and $\widehat{{\cal K}}_i$ 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 $\bar{B} \to D^{(*)} \tau^- \bar{\nu}_\tau$ decays has obvious effects on the angular observables $\widehat{{\cal K}}_i (q^2)$, except $\widehat{{\cal K}}_{1ss} (q^2)$ and $\widehat{{\cal K}}_{1cc} (q^2)$.