Multi-Period Fermi-LAT and LHAASO Constraints on Axion-Like Particles from Mrk 421 via ${\chi }^2$ Profile Likelihood with Gaussian Copula Correlation

Abstract

We present a joint multi-period analysis of axion-like 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 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 ($m_a\lesssim 1$\,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 multi-messenger gamma-ray data.

arXiv commentAlready accepted by Physical Review D