This paper presents a measurement of the polarisation
of τ leptons produced in Z/γ ∗ → τ τ decays which
is performed with a dataset of proton—proton collisions at
√s = 8 TeV, corresponding to an integrated luminosity of
20.2 fb−1 recorded with the ATLAS detector at the LHC
in 2012. The Z/γ ∗ → τ τ decays are reconstructed from a
hadronically decaying τ lepton with a single charged particle
in the final state, accompanied by a τ lepton that decays
leptonically. The τ polarisation is inferred from the relative
fraction of energy carried by charged and neutral hadrons in
the hadronic τ decays. The polarisation is measured in a fiducial
region that corresponds to the kinematic region accessible
to this analysis. The τ polarisation extracted over the full
phase space within the Z/γ ∗ mass range of 66 < mZ/γ ∗ <
116 GeV is found to be Pτ = −0.14±0.02(stat)±0.04(syst).
It is in agreement with the Standard Model prediction of
Pτ = −0.1517 ± 0.0019, which is obtained from the ALPGEN
event generator interfaced with the PYTHIA 6 parton
shower modelling and the TAUOLA τ decay library.