Determining the CP parity of Higgs bosons at the LHC in the $\tau$ to 1-prong decay channels

We propose a method for determining the CP nature of a neutral Higgs boson or spin-zero resonance $\phi$ at the CERN Large Hadron Collider (LHC) in its $\phi\to\tau^{-}\tau^{+}$ decay channel. The method can be applied to any 1-prong $\tau$-decay mode, which comprise the majority of the $\tau$-lepton decays. The proposed observables allow to discriminate between pure scalar and pseudoscalar Higgs-boson states and/or between a CP-conserving and CP-violating Higgs sector. We show for the decays $\tau\to\pi\nu_{\tau}$ that the method maintains its discriminating power when measurement uncertainties are taken into account. The method will be applicable also at a future linear $e^{+}e^{-}$ collider.