Probing $WW\gamma$ coupling through $e^- \gamma \rightarrow \nu_e W^-$ at ILC

The anomalous $WW\gamma$ coupling is probed through $e\gamma\rightarrow \nu W$ at the ILC. With a spectacular single lepton final state, this process is well suited to study the above coupling. Cross section measurements can probe $\delta \kappa_\gamma$ to about $\pm 0.004$ for a luminosity of 100 fb$^{-1}$ at $500$ GeV center-of-mass energy with unpolarized electron beam. The limits derivable on $\lambda_\gamma$ from the total cross section are comparatively more relaxed. Exploiting the energy-angle double distribution of the secondary muons, kinematic regions sensitive to these couplings are identified. The derivable limit on $\lambda_\gamma < 0$ could be improved to a few per-mil, focusing on such regions. More importantly, the angular distributions at fixed energy values, and energy distribution at fixed angles present very interesting possibility of distinguishing the case of $\lambda_\gamma <0$ and $\lambda_\gamma \ge 0$.