  We present a new calculation of axion-like particle (ALP) production in the
semi-exclusive photon-initiated (PI) channel, that is either with intact
outgoing protons or rapidity gaps present in the final state, and with no
colour flow between the colliding LHC protons. This is the first full treatment
of this process, accounting for both the possibility of proton dissociation and
the survival factor probability of no additional proton-proton interactions,
including its kinematic and process dependence. We present the expected event
yields in the case that either one or both protons are required to be
registered in the forward proton detectors installed in association with ATLAS
and CMS. We find that this process can be sensitive to currently unprobed
regions of ALP mass and ALP-photon coupling, in particular in the intermediate
mass region. Our calculation is provided in the publicly available SuperChic 4
Monte Carlo (MC) generator, and can be passed to a general purpose MC for
showering and hadronization of the final state.
