TauPolaris: reconstructing tau lepton polarimetric vectors with conditional normalizing flows
The kinematics of tau lepton decay products depend on the tau spin, giving access to the spin correlations and CP structure of the process that produced them. The optimal spin observable is the polarimetric vector, which points along the most likely direction of the tau spin. Determining it requires the momenta of the neutrinos produced in the tau decays, which escape detection and must therefore be inferred. We present TauPolaris, a tool for reconstructing tau polarimetric vectors by estimating the undetected neutrino momenta with a conditional normalizing flow. Rather than performing a point regression, the method models the full conditional density of the neutrino kinematics, providing both the most likely configuration for each event and an estimate of its uncertainty. The resolution of the reconstructed spin observables improves on that obtained from networks trained with a mean-squared-error loss. Using simulated LHC proton-proton collisions, including detector resolution effects, we demonstrate the method in three applications. For tau leptons produced in Higgs boson decays, we show that the presence of quantum entanglement can be distinguished from its absence with a significance of at least $4.3\sigma$ at the High-Luminosity LHC. We demonstrate an 18% improvement in the sensitivity to CP violation in $H\rightarrow\tau\tau$ decays. Finally, we introduce new variables for suppressing the $Z\rightarrow\tau\tau$ background in Higgs boson searches.