Searching for Axion-Like Particles with MAGIC and Fermi-LAT Data.

In this work, we reanalyze the axion-like particle (ALP)-photon oscillation effect in the $\gamma$-ray spectra of the blazars Markarian 421 (Mrk 421) and PG 1553+113 using the Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) and Fermi Large Area Telescope (Fermi-LAT) data. These data are collected during the common operation time, which cover twenty activity phases of these blazars. Not all the observations of these phases can be individually used to set the 95% confidence level ($\rm C.L.$) constraint on the ALP parameter space. However, the constraint can be significantly improved if the analyses for the observations of these phases are combined. We release the combined constraints results of the sources Mrk 421 with fifteen phases and PG 1553+113 with five phases, respectively. For Mrk 421, we find that the $\gamma$-ray observations of MAGIC and Fermi-LAT have excluded the ALP parameter region with the ALP-photon coupling of $g_{a\gamma} \gtrsim 2 \times 10^{-11}$ $\rm GeV^{-1}$ for the ALP mass of $\sim 8\times 10^{-9}$ eV $\lesssim m_a \lesssim 2\times 10^{-7}$ eV at 95% $\rm C.L.$ However, we find that the ALP-photon oscillation would improve the fit to the observed spectra of PG 1553+113 and find some favored parameter regions at 95% $\rm C.L.$