Semi-leptonic four-fermion final states in polarised γγ reactions: Exact results vs an improved narrow width approximation

We calculate the process $\gamma \gamma \rightarrow e^- \bar{\nu}_e u \bar{d}$ with the full set of Feynman diagrams. We consider different implementations of the $W$ width and different combinations of the photon polarisations. The results of an improved narrow width approximation based on $\gamma \gamma \rightarrow W^+ W^-$ with full spin-correlations that takes into account different angular cuts as well as cuts on the invariant masses are compared to those of the complete calculation.