How to use SANC to improve the PHOTOS Monte Carlo simulation of bremsstrahlung in leptonic W-Boson decays

Using the SANC system we study the one-loop electroweak standard model predictions, including virtual and real photon emission, for the decays of the on-shell vector boson, $W \to l {\nu_l} (\gamma)$. The complete one-loop corrections and exact photon emission matrix element are taken into account. For the phase-space integration, the Monte Carlo technique is used. This provides a useful element, first for the evaluation of the theoretical uncertainty of PHOTOS. Later we analyse the source of the differences between SANC and PHOTOS and we calculate the additional weight, which once installed, improves predictions of PHOTOS simulations. We can conclude that, after the correction of the weight is implemented, the theoretical uncertainty of PHOTOS simulations due to an incomplete first-order matrix element is reduced to below $\alpha \over \pi$, for observables not tagging the photon in a direct way, and to 10% otherwise. This is interesting for applications in the phenomenology of the ongoing LEP2 and future LC and LHC experimental studies.