T-odd Asymmetry in W+jet Events at the LHC

W bosons produced at high transverse momentum in hadron collisions can have polarization along the direction perpendicular to the production plane, which is odd under na$\ddot{\i}$ve-T-reversal where both the three-momenta and angular momenta are reversed. Perturbative QCD predicts non-zero polarization at the one-loop level, which can be measured as parity-odd components in the angular distribution of charged leptons from the decay of W bosons. We perform a detector-level simulation with the generator MadGraph5_aMC@NLO, and demonstrate that the asymmetry can be observed at the 8 TeV LHC with 20 fb$^{-1}$ of data. If confirmed, it will be the first experimental measurement of the sign of the imaginary part of one-loop QCD amplitudes.