  The existence of an axion-like particle (ALP) would induce anomalous
scattering of light by light. This process can be probed at the Large Hadron
Collider in central exclusive production of photon pairs in proton-proton
collisions by tagging the surviving protons using forward proton detectors.
Using a detailed simulation, we estimate the expected bounds on the ALP--photon
coupling for a wide range of masses. We show that the proposed search is
competitive and complementary to other collider bounds for masses above 600
GeV, especially for resonant ALP production between 600 GeV and 2 TeV. Our
results are also valid for a CP-even scalar, and the efficiency of the search
is independent of the width of the ALP.
