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If neutral Higgs bosons will be discovered at the CERN Large Hadron Collider(LHC) then an important subsequent issue will be the investigation of their CPnature. Higgs boson decays into tau lepton pairs are particularly suited inthis respect. Analyzing the three charged pion decay modes of the tau leptonsand taking expected measurement uncertainties at the LHC into account, we showthat the CP properties of a Higgs boson can be pinned down with appropriatelychosen observables, provided that sufficiently large event numbers willeventually be available.

Determining the CP parity of Higgs bosons at the LHC in their tau decay channels