First search for exclusive diphoton production at high mass with intact protons in proton-proton collisions at $\sqrt{s} = 13~\mathrm{TeV}$ at the LHC

A search for exclusive two-photon production via photon exchange in proton-proton collisions, $pp\to p\gamma\gamma p$ with intact protons, is presented. The data correspond to an integrated luminosity of 9.4 fb$^{-1}$ collected in 2016 at a center-of-mass energy of 13$~\mathrm{TeV}$ under LHC standard luminosity conditions. Events are selected with a diphoton invariant mass above 350$~\mathrm{GeV}$ and with both protons intact in the final state to reduce dominant backgrounds from strong interactions. The events of interest correspond to those where the momentum loss observed for the intact, forward-moving protons equals the invariant mass deduced for the central, two photon system. No events are found that satisfy this condition. Using an effective dimension-8 extension of the standard model, this result allows the first limits to be set on anomalous four-photon coupling parameters, with $\mid\zeta_1\mid<3.7\times10^{-13}~\mathrm{GeV}^{-4}$ and $\mid\zeta_2\mid<7.7\times10^{-13}~\mathrm{GeV}^{-4}$.