CP violating anomalous couplings in $W$ jet production at the LHC

T-odd correlations in $Wj$ production at the LHC have been studied recently as a way to measure a phase produced by QCD at NLO by Frederix et. al. That study found that the induced asymmetry could be observed with 20 fb$^{-1}$ of 8 TeV data. These T-odd asymmetries can also be induced by CP violating new physics interfering with the SM at LO. In this paper we study this possibility using effective Lagrangians to describe the new physics. We find that the leading contribution arises at dimension eight, and that it necessarily introduces flavor changing neutral currents as well. We discuss the constraints that can be placed on the flavor structure of the new physics operator from studies of FCNC in kaon and B meson decays and then compare the T-odd correlations in $Wj$ induced by CP violating new physics to those induced by QCD at NLO. We quantify the level at which these couplings can be probed at the LHC, and find that they will not affect a measurement of the NLO QCD phases.