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Anomalous $WWγ$ couplings with beam polarization at the Compact Linear Collider

We study the anomalous $WWγ$ couplings at the Compact Linear Collider through the processes $e^{+}e^{-}\to W^+W^-$, $e^{-}e^{+} \to e^{-} γ^{*} e^{+} \to e^{+} ν_{e} W^-$ and $e^{-}e^{+}\to e^{-} γ^{*} γ^{*} e^{+} \to e^{-} W^+ W^- e^{+} $ $ (γ^{*}$ is the Weizsacker-Williams photon). We give the 95\% confidence level limits for unpolarized and polarized electron (positron) beam on the anomalous couplings for various values of the integrated luminosities and center-of-mass energies. We show that the obtained limits on the anomalous couplings through these processes can highly improve the current experimental limits. In addition, our limits with beam polarization are approximately two times better than the unpolarized case.