  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.
