Markarian421 is a well-known nearby BL Lac blazar at the redshift z=0.031. Many previous works were investigated to constrain the axion-photon coupling from its TeV gamma-ray observations, showing the upper limit on the coupling constant gaγ≲2.0×10−11GeV−1 for the axion mass [5.0×10−10eV≲ma≲5.0×10−7eV]. While in this work, we obtain a more stringent upper limit on the axion-photon coupling from the 1038 days gamma-ray observations of the blazar Markarian421. The long-term VHE gamma-ray spectra are measured by the collaborations Large Area Telescope on board NASA's Fermi Gamma-ray Space Telescope (Fermi-LAT) and High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory from 2015 June to 2018 July. We show the best-fit spectral energy distributions (SEDs) of Markarian421 under the null and axion hypotheses. Then we set the axion-photon limit in the {ma,gaγ} plane. The 99% C.L. upper limit set by Markarian421 is gaγ≲4.0×10−12GeV−1 for the axion mass [1.0×10−9eV≲ma≲1.0×10−8eV]. It is the most stringent upper limit in this axion mass region.
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