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Reconstruction and classification of tau lepton decays with ILD

Tau-lepton decays with up to two $π^0$'s in the final state, $τ^+ \to π^+ \barν_τ$, $ρ^+ (π^+π^0) \barν_τ$, $a^+_1 (π^+π^0π^0) \barν_τ$, are used to study the performance of the barrel part of the silicon-tungsten electromagnetic calorimeter (Si-W ECAL) of the International Large Detector (ILD) at the future $e^+-e^-$ International Linear Collider. A correct reconstruction of the tau decay mode is crucial for constraining the tau spin state and measuring the Higgs boson CP state in $H\to τ^+τ^-$ decays. About 95% of $π^+ \barν_τ$ and 90% of $ρ^+\barν_τ$ and $a^+_1\barν_τ$ decays from $e^+e^-\to Z^0\to τ^+τ^-$ reaction at $e^\pm$-beam energy of 125 GeV are correctly reconstructed. In a smaller ILD detector, with Si-W ECAL radius reduced by about 20% these numbers degrade by at most 2%. The $π^0$ mass resolution stays below 10%. Since the failures in the tau-lepton reconstruction are mainly due to photons, the increase of the ILD magnetic field from 3.5 T to 4 T does not bring any significant improvement.