  By tagging one or two intact protons in the forward direction, it is possible
to select and measure exclusive photon-fusion processes at the LHC. The same
processes can also be measured in heavy ion collisions, and are often denoted
as ultraperipheral collisions (UPC) processes. Such measurements open up the
possibility of probing certain dimension-8 operators and their positivity
bounds at the LHC. As a demonstration, we perform a phenomenological study on
the $\gamma\gamma\to \ell^+\ell^-$ processes, and find out that the
measurements of this process at the HL-LHC provide reaches on a set of
dimension-8 operator coefficients that are comparable to the ones at future
lepton colliders. We also point out that the $\gamma q\to \gamma q$ process
could potentially have better reaches on similar types of operators due to its
larger cross section, but a more detailed experimental study is need to
estimate the signal and background rates of this process. The validity of
effective field theory (EFT) and the robustness of the positivity
interpretation are also discussed.
