Four Fermions Productions at a $\gamma\gamma$ Collider

Using the recently proposed ALPHA algorithm (and the resulting code) I compute the rate (at tree level) for the process $\gamma\gamma\rightarrow\bar\nu_e e^- u \bar d$. The bulk of the contribution is due to W pair production and decay. However a non negligible ($\sim10 \%$) contribution comes from other channels, mainly the production and decay of a W and a collinear charged fermion. Requiring that the reconstructed invariant $u \bar d$ mass lies in the intervals $M_W\pm 5$ GeV and $M_W\pm 20$ GeV one obtains a rate which is lower, by 25 \% and 4 \% respectively, than the rate obtained in the $narrow$ $width$ approximation, thus demonstrating the relevance of the finite W width.