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Anomalous trilinear and quartic $WWγ$, $WWγγ$, $ZZγ$ and $ZZγγ$ couplings in photon induced processes at the LHC

We first report on possible measurements at the LHC using the first data and a luminosity of 10 pb$^{-1}$ of $W$ and $Z$ pair production via two-photon exchange. This measurement allows in particular to increase the present sensitivity on $WWγγ$ and $ZZγγ$ quartic anomalous couplings from the LEP experiments by almost three orders of magnitude. We also discuss the possible improvements on quartic and trilinear anomalous couplings at high luminosity at the LHC using new forward proton taggers to be installed at 220 and 420 m from the CMS or ATLAS detectors.