Measurement of the effective leptonic weak mixing angle using electron and muon pairs from $Z$-boson decay in the ATLAS experiment at $\sqrt s = 8$ TeV

This note presents a measurement of the effective leptonic weak mixing angle by the ATLAS experiment, based on data collected in 2012 at~$\sqrt s = 8$~TeV at the LHC collider and corresponding to an integrated luminosity of~20.1~\ifb. The combination of 6~million electron and 7.5~million muon pairs from $Z$-boson decays in the central region, complemented by 1.5~million electron pairs with one electron in the forward region of the detector, leads to optimal sensitivity to the weak mixing angle. This measurement extends a previous measurement of the full set of angular coefficients from $Z$-boson decay. It consists of a set of measurements of the angular coefficient most sensitive to the weak mixing angle, binned in dilepton mass and rapidity, such as to simultaneously reduce considerably the dominant source of systematic uncertainties arising from parton distribution functions (PDF) when interpreting the measurements to extract the value of the effective leptonic weak mixing angle. The impact of electroweak virtual corrections on the interpretation of the measurements is also precisely evaluated using the legacy framework from the LEP era. The effective leptonic weak mixing angle is measured to be $0.23140 \pm\ 0.00021$~(stat.)~$\pm\ 0.00024$~(PDF)~$\pm\ 0.00016$~(syst.), where the first uncertainty corresponds to data statistics, the second to the overall impact of PDFs, and the third to all other systematic uncertainties affecting the measurement and its interpretation. This result agrees within its total uncertainty of~$\pm 0.00036$ with the current world average of~$0.23150 \pm\ 0.00006$ from global electroweak fits.