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CP violating anomalous couplings in $Wγ$ and $Zγ$ production at the LHC

The ATLAS and CMS collaborations have recently published new limits on CP conserving anomalous couplings from the $Wγ$ and $Zγ$ production processes. We study the corresponding limits that can be placed on the CP violating anomalous couplings $κ_tilde_γ$ and $h^1_{γ, Z}$ at the LHC. We find that the process $pp --> Wγ$ at 14 TeV can place the 95% CL limit $|κ_tilde_γ| <~ 0.05$ with 10 fb^{-1} which is comparable to the existing LHC bound on the CP conserving anomalous couplings $κ_γ$. Similarly, the process $pp --> Zγ$ can place the 95% CL limits $|h^1_γ| <~ 20$ and $|h^1_Z| <~ 40$ respectively. None of these limits is derived from a truly CP-odd observable so that it is not possible to separate the effects of the CP violating anomalous couplings from the rest.