Sensitivity physics expected to the measurement of the quartic WWγγ couplings at the LHeC and the FCC-he

We explore the physics expected sensitivity at the Large Hadron electron Collider (LHeC) and the future circular collider-hadron electron ( FCC-he) to search for the anomalous quartic WW gamma gamma couplings in single W-boson production in association with a photon. We study the process ep -> e(-)gamma*p -> eW gamma q'X via the subprocess gamma*q -> W gamma q'. The center-of-mass energies and luminosities of the LHeC are assumed to be root s = 1.30, 1.98 TeV, L = 10 - 100 fb(-1) and for the FCC-he root s = 3.46, 5.29 TeV and L = 100 - 1000 fb(-1). Considering these energies and luminosities, we estimate sensitivity measures on the anomalous quartic WW gamma gamma couplings at 95% C.L., which can be an order of magnitude more stringent than the experimental limits reported by ATLAS and CMS Collaborations at the LHC.