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

We consider the largest observed sample including all intermediate-frequency peaked (IBL) and high-frequency peaked (HBL) flaring blazars above 100 GeV up to redshift $z = 0.6$. We show that the best-fit regression line of the emitted spectral 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 our expectation that such a distribution should be $z$-independent. We argue that the above correlation does not arise from any selection bias. We show that our expectation naturally emerges provided that axion-like particles (ALPs) are put into the game. Moreover, ALPs can also explain why flat spectrum radio quasars emit up to 400 GeV, in sharp contradiction with conventional physics. So, the combination of the two very different but consistent results -- taken at face value -- leads to a hint at an ALP with mass $m = {\cal O} (10^{-10} \, {\rm eV})$ and two-photon coupling in the range $2.94 \times 10^{- 12} \, {\rm GeV}^{- 1} < g_{a \gamma \gamma} < 0.66 \times 10^{- 10} \, {\rm GeV}^{- 1}$. As a bonus, the Universe would become considerably more transparent above energies $E \gtrsim 1 \, {\rm TeV}$ than dictated by conventional physics. Our prediction can be checked not only by the new generation of observatories like CTA, HAWC, GAMMA-400, LHAASO, TAIGA-HiSCORE and HERD, but also thanks to the planned laboratory experiments ALPS II (upgraded), STAX, IAXO and with other techniques now being developed by Avignone and collaborators.