The measurable angular distribution of {Lambda}_b^0to {Lambda}_c^{+}left(to {Lambda}^0{pi}^{+}right){tau}^{-}left(to {pi}^{-}{v}_{tau}right){overline{v}}_{tau } decay

Abstract

In {Lambda}_b^0to {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^0to {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}}_ileft({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}^2right) and the forward-backward asymmetry of π− meson AFB(q2), both of which can be represented by the angular observables {hat{mathcal{K}}}_ileft({q}^2right) . We provide numerical results for the entire set of the angular observables {hat{mathcal{K}}}_ileft({q}^2right) 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}}}_ileft({q}^2right) , except {hat{mathcal{K}}}_{1 ss}left({q}^2right) and {hat{mathcal{K}}}_{1 cc}left({q}^2right) .