$T$-Odd Asymmetry in $W+\mathbf{\text{jet}}$ 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 naïve $T$ reversal where both the three-momenta and angular momenta are reversed. Perturbative QCD predicts nonzero 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 $20{\mathrm{fb}}^{-1}$ of data. If confirmed, it will be the first experimental measurement of the sign of the imaginary part of one-loop QCD amplitudes.

Figure 1

$x_l^{\perp }=p_l^{\perp }/(M_W/2)$ distributions for the $W+\text{jet}$ events after the selection cuts (a–e) and a cut of $\mathrm{\Delta }\eta >1.0$, at the 8 TeV LHC, in the leading-order calculation at the parton level. Predictions for $x_l^{\perp }>0$ and $x_l^{\perp }<0$ regions are separately plotted in the red solid and blue dashed lines, respectively.

Figure 2

$\mathrm{\Delta }\eta$ distributions for the cross section (left), left-right difference of the cross section (middle), and the left-right asymmetry (right) at the 8 TeV LHC after the selection cuts and a cut of $|x_l^{\perp }|>0.6$. Results by the MadGraph5_aMC@NLO and LOMC simulations are shown in dark-colored and light-colored histograms, respectively, with scale uncertainties.