Searching for axion-like particles with the blazar observations of MAGIC and Fermi-LAT *

We explore the axion-like particle (ALP)-photon oscillation effect in $\gamma$-ray spectra of blazars Markarian 421 (Mrk 421) and PG 1553+113, which are measured by Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) Fermi Large Area Telescope (Fermi-LAT) with high precision. investigate constraints on ALP parameter space using Mrk 1553+113 observations 15 5 phases, respectively. find that combined analysis all phases improves limits from observations. The limit set has excluded region ALP-photon coupling $g_{a\gamma} \gtrsim 2 \times 10^{-11} \, \rm GeV^{-1}$ for mass $\sim 8\times 10^{-9}\, {\rm eV} \lesssim m_a 2\times 10^{-7}\rm eV$ at 95% $\rm C.L.$ also hypothesis can slightly improve fit to results some regions, do not this case.