$WW\gamma$ production at hadron colliders with NLO QCD+EW corrections and parton shower effects

W+W-gamma production in proton-proton collision provides a window to the mechanism of electroweak symmetry breaking and a direct accessment to triple and quartic gauge couplings. Precision study of gauge boson self-interactions may also provide evidence of existence of new physics beyond the standard model. In this paper, we study the W+W-gamma production at the LHC and future higher energy proton-proton colliders at the QCD+EW NLO including parton shower effects. We find that the contributions from the photon-induced (i.e. q gamma- and gamma gamma-initiated) channels are non-negligible since the photon luminosity can be enhanced significantly with the increment of colliding energy, and the large real jet emission QCD and EW corrections can be depressed sufficiently by applying the jet veto event selection scheme. Moreover, we also investigate the theoretical errors arising from the PDF uncertainty and the factorization/renormalization scale dependence.