ILD benchmark: a study of $e^- e^+ to tau^- tau^+$ at 500 GeV

The process $e^- e^+ to tau^- tau^+$ is of particular interest because the tau lepton polarisation can be reconstructed, allowing its chiral nature to be probed. This note reports on a study of the reconstruction of the di-tau final state at ILC-500, its selection and the reduction of backgrounds, the identification of the tau leptons decay mode, and on the extraction of the tau leptons polarisation. The performance of this analysis is studied in two models of the ILD detector, one larger (IDR-L) the other smaller (IDR-S), which differ in the outer radius of the TPC and of the subdetectors beyond, and in the magnetic field strength of the detector solenoid. We find that the high-mass tau-pair events in which at least one tau decays haronically can be selected with an efficiency of around 60%, with a remaining background from non-di-tau processes at the few-% level. Single-prong decay modes $tau^pm to pi^pm u, tau^pm to pi^pm pi^0 u, tau^pm to pi^pm pi^0 pi^0 u$ can be correctly identified in around 60-90% of cases, with sample purities in the range 50-90%, depending on decay mode. The sensitivity to tau polarisation was estimated in the four beam polarisation datasets envisaged for the $4 ab^{-1}$ of data forseen for ILC-500. Statistical precisions on the polarisation in the different datasets are predicted to be between 0.5 and 2%. While some small performance differences between the two detector models are seen, they have very similar final sensitivity to the polarisation measurement.