We present a joint multi-period analysis of axionlike particles (ALPs) using five sets of simultaneous Fermi-LAT and LHAASO observations of the TeV blazar Mrk 421. Photon-ALP oscillations are calculated self-consistently together with extragalactic background light (EBL) absorption for two representative jet emission models: a two-zone hybrid model and a single-zone hadronic model. To account for weak correlations among different observational epochs, we adopt a ${\chi }^2$-based profile analysis combined with a Gaussian copula ($\rho =0.03$). Nuisance parameters are optimized under the no-ALP hypothesis before profiling the ALP parameters $m_a$ and $g_{a\gamma }$. In the low-mass regime ($m_a\lesssim 1\mathrm{neV}$) we obtain a 95% CL upper limit of $g_{a\gamma }=6.35\times {10}^{-13}{\mathrm{GeV}}^{-1}$. Over the full mass range 0.1–500 neV, the most conservative 95% CL upper limits are $g_{a\gamma }<6.69\times {10}^{-12}{\mathrm{GeV}}^{-1}$ (two zone) and $g_{a\gamma }<7.37\times {10}^{-12}{\mathrm{GeV}}^{-1}$ (single zone). Variations of the EBL template, the Galactic and intergalactic magnetic-field models, the spectral binning, and residual instrumental systematics change these limits by only a few percent. The jet magnetic field is the leading systematic and can shift the low-mass bound by a factor of a few; only a substantially weaker single-zone field degrades the constraint by about an order of magnitude. The analysis framework developed here provides a statistically consistent approach for future ALP searches with multimessenger gamma-ray data.

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• Particle astrophysics