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We consider the largest observed sample including all intermediate-frequencypeaked (IBL) and high-frequency peaked (HBL) flaring blazars above 100 GeV upto redshift $z = 0.6$. We show that the best-fit regression line of the emittedspectral indices $\Gamma_{\rm em} (z)$ is a concave parabola decreasing as $z$increases, thereby implying a statistical correlation between the$\{\Gamma_{\rm em} (z) \}$ distribution and $z$. This result contradicts ourexpectation that such a distribution should be $z$-independent. We argue thatthe above correlation does not arise from any selection bias. We show that ourexpectation naturally emerges provided that axion-like particles (ALPs) are putinto the game. Moreover, ALPs can also explain why flat spectrum radio quasarsemit up to 400 GeV, in sharp contradiction with conventional physics. So, thecombination of the two very different but consistent results -- taken at facevalue -- leads to a hint at an ALP with mass $m = {\cal O} (10^{-10} \, {\rmeV})$ and two-photon coupling in the range $2.94 \times 10^{- 12} \, {\rmGeV}^{- 1} < g_{a \gamma \gamma} < 0.66 \times 10^{- 10} \, {\rm GeV}^{- 1}$.As a bonus, the Universe would become considerably more transparent aboveenergies $E \gtrsim 1 \, {\rm TeV}$ than dictated by conventional physics. Ourprediction can be checked not only by the new generation of observatories likeCTA, HAWC, GAMMA-400, LHAASO, TAIGA-HiSCORE and HERD, but also thanks to theplanned laboratory experiments ALPS II (upgraded), STAX, IAXO and with othertechniques now being developed by Avignone and collaborators.

Hint at an axion-like particle from the redshift dependence of blazar spectra