Determination of the tau energy scale and the associated systematic uncertainty in proton-proton collisions at $\sqrt{s}=8\;\textrm{TeV}$ with the ATLAS detector at the LHC in 2012

This note describes the energy scale calibration of hadronic $\tau$ decays and the associated uncertainty in 4.5 fb$^{-1}$ of data at $\sqrt{s}=8$ TeV recorded in 2012 with the ATLAS detector at the LHC. The calibration is based on simulated $\tau$ decays, while the systematic uncertainty is estimated by propagating single particle response measurements to the individual $\tau$ decay products, namely charged and neutral pions. The systematic uncertainty on the hadronic $\tau$ energy scale for $p^{\tau}_T>20$ GeV and $|\eta^{\tau}|<2.5$ is found to be $ \leq 3\%$ for the hadronic decay modes with exactly one reconstructed track, and $\leq 4\%$ for the hadronic decay modes with at least two reconstructed tracks. The systematic uncertainty is obtained with a deconvolution method, and is checked using an in-situ analysis of the visible mass of reconstructed $Z$ boson decays into one leptonically and one hadronically decaying $\tau$. These two methods yield results that are compatible within the calculated uncertainties.