Search for the imprint of axion-like particles in the highest-energy photons of hard $\gamma$-ray blazars

Axion-like particles (ALPs), predicted in theories beyond the Standard Model, can have observational effects on the transparency of the Universe to $\gamma$ rays in the presence of magnetic fields. In this work, we search for effects compatible with the existence of ALPs with 80 months of data from the ${\it Fermi}$ Large Area Telescope, by comparing the distributions of observed highest energy photons from sources beyond redshifts of z $\geq$ 0.1 with theoretical predictions in the presence of ALPs. We find no evidence for an increased $\gamma$-ray transparency due to ALPs and therefore we set limits on the ALPs parameters assuming a value of the intergalactic magnetic field strength of 1 nG. Photon-ALP couplings above $10^{-11}$ GeV$^{-1}$ are excluded for ALP masses $m_{a}$ $\lesssim3.0$ neV. These limits exclude a region of the parameter space not covered by other $\gamma$-ray telescopes and are compatible with constraints imposed by other experiments.