QED bremsstrahlung in decays of electroweak bosons

Isolated lepton momenta, in particular their directions are the most precisely measured quantities in pp collisions at LHC. This offers opportunities for multitude of precision measurements. It is of practical importance to verify if precision measurements with leptons in the final state require all theoretical effects evaluated simultaneously or if QED bremsstrahlung in the final state can be separated without unwanted precision loss. Results for final-state bremsstrahlung in the decays of narrow resonances are obtained from the Feynman rules of QED in an unambiguous way and can be controlled with a very high precision. Also for resonances of non-negligible width, if calculations are appropriately performed, such separation from the remaining electroweak effects can be expected. Our paper is devoted to validation that final-state QED bremsstrahlung can indeed be separated from the rest of QCD and electroweak effects, in the production and decay of Z and W bosons, and to estimation of the resulting systematic error. The quantitative discussion is based on Monte Carlo programs PHOTOS and SANC, as well as on KKMC which is used for benchmark results. We show that for a large class of W and Z boson observables as used at LHC, the theoretical error on photonic bremsstrahlung is 0.1 or 0.2 %, depending on the program options used. An overall theoretical error on the QED final-state radiation, i.e. taking into account missing corrections due to pair emission and interference with initial state radiation is estimated respectively at 0.2 % or 0.3 % again depending on the program option used.