2025MNRAS.536.3242O

The gamma-ray emission in blazars can be attributed to the leptonic synchrotron self-Compton (SSC) model, photohadronic interactions, or a combination thereof. While evidence supports both models, their specific contributions remain uncertain. One supportive piece of evidence for the SSC model is the correlation between synchrotron and SSC fluxes in some blazar's spectral energy distribution (SED), indicating the relative contributions of leptonic and hadronic mechanisms. Observational studies of the high-synchrotron peaked BL Lac (HBL) blazar Markarian 421 over several years, spanning TeV gamma-rays and X-rays, have reported a linear correlation across various time-scales, which breaks at the highest gamma-ray fluxes. Extending this analysis to four HBL blazars - Markarian 501, 1ES 1959+650, PKS 2155-304, and 1ES 2344+514 - we utilize multiwavelength data from ground-based Imaging Atmospheric Cherenkov Telescopes for gamma-rays and satellite observations for X-rays. Our long-term study confirms a linear correlation between fluxes across these energy bands, except for Markarian 501, which shows a correlation index of $1.45 \pm 0.01$. Notably, the exceptional flaring episode of PKS 2155-304 exhibits a correlation index of 2 with extreme values of gamma-ray fluxes. We observe outliers with high gamma-ray fluxes, suggesting the involvement of another mechanism, either of hadronic or leptonic origin. Finally, all other correlations exhibit alignment with a general correlation, suggesting a common acceleration mechanism among them with slight variations likely due to individual magnetic field strengths.