Measurement of the transverse spin correlations in the decay $Z \rightarrow \tau^+\tau^-$

For tau leptons produced in e^+e^- -> tau^+ tau^- interactions there are, in addition to the longitudinal spin correlations, two independent transverse spin correlations associated with the transverse (within the production plane) and normal (to the production plane) polarization components. A measurement of the transverse-transverse and transverse-normal tau spin correlations in the decay Z -> tau^+ tau^-, C_{TT} and C_{TN}, is presented based on the aplanarity angle of the decay products of both tau leptons. Using 80 pb^{-1} of data collected by ALEPH on the peak of the Z resonance, the results are C_{TT} = 1.06 +- 0.13 (stat) +- 0.05 (syst), and C_{TN} = 0.08 +- 0.13 (stat) +- 0.04 (syst). These values are in agreement with the Standard Model predictions, C_{TT} = 0.99 and C_{TN} = -0.01