Upper limit on axion-photon coupling from Markarian 421

We obtain a stringent upper limit on axion-photon coupling from the 1038 days gamma-ray observations of the TeV blazar Markarian 421. The long-term VHE gamma-ray spectra are measured by the collaborations Fermi-LAT and HAWC from 2015 June to 2018 July. We show the best-fit SEDs of Markarian 421 under the null and axion hypotheses. Then we set the axion-photon limit in the ₐ, \, gaγ\ plane. The 99% C.L. upper limit set by Markarian 421 is gaγ 4.0× 10⁻¹² \, GeV⁻¹ for the axion mass [1.0×10⁻⁹ \, eV mₐ 1.0×10⁻⁸ \, eV]. It is the most stringent upper limit in this axion mass region.