Extragalactic photon-axion-like particle oscillations up to 1000 TeV

Axion-like particles (ALPs) are attracting increasing interest since, among other things, they are a prediction of many extensions of the standard model of elementary particles physics and in particular of superstrings and superbranes. ALPs are very light, neutral, pseudo-scalar bosons which are supposed to interact with two photons. For their mass m_a ≪ 1 eV and two-photon coupling g_γγa in a suitable range they can give rise to very interesting astrophysical effects taking place in the X- and γ-ray bands. Specifically, throughout the present paper we are concerned with photon-ALP oscillations in the very-high-energy band (VHE , 100 GeV ≲ E ≲ 100 TeV) and beyond, which ought to occur in the photon beam emitted by far-away blazars and are triggered by the domain-like random extragalactic magnetic field B_ext. Because of the presence of the extragalactic background light (EBL) - which is the infrared/optical/ultraviolet radiation emitted by all galaxies during the cosmic evolution - when a VHE photon scatters off an EBL photon an e⁺e^- pair can be created, which causes a rather strong dimming of the source. In the presence of photon-ALP oscillation things are different, since a photon travels sometimes as a true photon and sometimes as an ALP. Since ALPs do not interact with the EBL, the effective optical depth is somewhat reduced. But - as a consequence - the photon survival probability gets strongly enhanced with respect to the prediction of conventional physics, thereby greatly increasing the photon transparency in the VHE band so that the corresponding horizon gets enlarged to a considerable extent. While all this is well known and already studied in detail (De Angelis et al., 2011, 2013a), the new effect of photon dispersion on the cosmic microwave background (CMB) becomes very important at high enough energies. The aim of the present paper is to take it systematically into account. Actually, two widely different energy scales are associated with it. One is E_H = O (5 TeV) , above which the effect in question starts to become dominant and makes the single random realizations of the beam propagation process - the only ones that are observable - to exhibit small energy oscillations: this is a crucial prediction of our model. The other energy scale is E_eq above which the oscillation length becomes smaller than the coherence length of B_ext: typically E_eq = O (40 TeV) with a large uncertainty. Thus, previously used domain-like models of B_ext would generally give wrong results above E_eq and a more realistic model for B_ext becomes compelling, like the one very recently developed by the authors. Remarkably, we have been able to derive the corresponding photon survival probability P_γ→γ^ALP (E₀ , z)analytically and exactly up to observed energies E₀ = 1000 TeV and redshift up to z = 2, a fact that drastically shortens the computation time in the derivation of the results presented in this paper. Specifically, for 7 simulated blazars we exhibit the plots of the P_γ→γ^ALP (E₀ , z) along 1000 random realizations versus E₀, for different values of z and four values of the model parameters. Our predictions can be tested by the new generation of γ-ray observatories like CTA, HAWC, GAMMA-400, LHAASO, TAIGA-HiSCORE and HERD. Finally, for our guessed values of m_a and g_γγa our ALP can be detected in the upgrade of ALPS II at DESY, the planned experiments IAXO, STAX and ABRACADABRA as well as with other techniques developed by Avignone and collaborators.