Probing the $WW\gamma$ Vertex in $e^\pm p\to\nu\gammaX$

We study the prospects of testing the $WW\gamma$ vertex in $e^- p\to\nu\gamma X$ and $e^+ p\to\nu\gamma X$ at HERA and LEP/LHC. Destructive interference effects between the Standard Model and the anomalous contributions to the amplitude severely limit the sensitivity of both processes to non-standard $WW\gamma$ couplings. Sensitivity limits for the anomalous $WW\gamma$ couplings $\kappa$ and $\lambda$ at HERA and LEP/LHC are derived, taking into account experimental cuts and uncertainties, and the form factor behaviour of nonstandard couplings. These limits are found to be significantly weaker than those which can be expected from other collider processes within the next few years. At HERA, they are comparable to bounds obtained from $S$-matrix unitarity.