Sensitivity analysis for the anomalous $$W^+W^-\gamma $$ couplings at the LHeC and the FCC-he

We study the anomalous $$W^+W^-\gamma $$ couplings in performing production of W-pair through process $$e^- p\,\rightarrow \,e^-\gamma ^*\gamma ^* \,e^-W^+W^-p$$ at Large Hadron electron Collider (LHeC) and Future Circular Collider-hadron (FCC-he). examine pure hadronic, semi-leptonic leptonic decay channels produced W-pair. assume center-of-mass energies $$\sqrt{s}=1.30$$ 1.98 TeV integrated luminosities 10–100 fb $$^{-1}$$ for LHeC $$\sqrt{s}=3.46$$ 5.29 100–2000 FCC-he. The best limits 95 $$\%$$ confidence level obtained $$\Delta \kappa _{\gamma }$$ $$\lambda are }=[-0.00208; 0.00206]$$ }=[- 0.00174; 0.00834]$$ . By comparing these with experimental limits, we present potentials future ep colliders.