Probing the CP nature of the Higgs boson at linear colliders with tau spin correlations; the case of mixed scalar--pseudoscalar couplings

The prospects for the measurement of the pseudoscalar admixture in the h-tau-tau coupling to a Standard Model Higgs boson of 120 GeV mass are discussed in a quantitative manner e+ e- collisions of 350 GeV centre-of-mass energy. Specific angular distributions in the h --> tau tau; tau --> rho nu decay chain can be used to probe mixing angles of scalar--pseudoscalar h-tau-tau couplings. In the discussion of the feasibility of the method, assumptions on the properties of a future detector for an e+ e- linear collider such as TESLA are used. The Standard Model Higgsstrahlung production process is taken as an example. For the expected performance of a typical Linear Collider set-up, the sensitivity of a measurement of the scalar--pseudoscalar mixing angle turned out to be 6 degree. It will be straightforward to apply our results to estimate the sensitivity of a measurement, in cases another scenario of the Higgs boson sector (Standard Model or not) is chosen by nature. The experimental error of the method is expected to be limited by the statistics.