Abstract
The sensitivities to anomalous quartic photon couplings at the Large Hadron Collider are estimated using diphoton production via photon fusion. The tagging of the protons proves to be a very powerful tool to suppress the background and unprecedented sensitivities down to $7\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}15}\text{ }{\mathrm{GeV}}^{\ensuremath{-}4}$ are obtained, providing a new window on extra dimensions and strongly interacting composite states in the multi-TeV range. Generic contributions to quartic photon couplings from charged and neutral particles with arbitrary spin are also presented.
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