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 $m_a\ll 1\mathrm{eV}$ and two-photon coupling $g_{\gamma \gamma a}$ 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 $(\mathrm{VHE},100\mathrm{GeV}\lesssim \mathcal{E}\lesssim 100\mathrm{TeV})$ 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 ${\mathbf{B}}_{\mathrm{ext}}$. 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 ${\mathcal{E}}_H=\mathcal{O}(5\mathrm{TeV})$, 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 ${\mathcal{E}}_{\mathrm{eq}}$ above which the oscillation length becomes smaller than the coherence length of ${\mathbf{B}}_{\mathrm{ext}}$: typically ${\mathcal{E}}_{\mathrm{eq}}=\mathcal{O}(40\mathrm{TeV})$ with a large uncertainty. Thus, previously used domain-like models of ${\mathbf{B}}_{\mathrm{ext}}$ would generally give wrong results above ${\mathcal{E}}_{\mathrm{eq}}$ and a more realistic model for ${\mathbf{B}}_{\mathrm{ext}}$ becomes compelling, like the one very recently developed by the authors. Remarkably, we have been able to derive the corresponding photon survival probability $P_{\gamma \to \gamma }^{\mathrm{ALP}}({\mathcal{E}}_0,z)$ analytically and exactly up to observed energies ${\mathcal{E}}_0=1000\mathrm{TeV}$ 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 $P_{\gamma \to \gamma }^{\mathrm{ALP}}({\mathcal{E}}_0,z)$ along 1000 random realizations versus ${\mathcal{E}}_0$, 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 $g_{\gamma \gamma a}$ 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.

由于轴突状粒子（ALP）是对基本粒子物理标准模型（尤其是超弦和超脑）的许多扩展的预测，因此受到越来越多的关注。ALP是非常轻的中性伪标量玻色子，应该与两个光子相互作用。为了他们的质量${米}_{\mathrm{一种}}\ll \mathrm{1个}\mathrm{电子伏特}$ 和两光子耦合 $G_{\gamma \gamma \mathrm{一种}}$在合适的范围内，它们会引起在X射线和γ射线波段发生的非常有趣的天体物理学效应。具体而言，在整个本文中，我们关注的是非常高能带中的光子-ALP振荡$（\mathrm{甚高频}，100\mathrm{GeV}\lesssim \mathcal{Ë}\lesssim 100\mathrm{电视}）$ 以及更远的距离，它们应该发生在遥远的天体发射的光子束中，并由类似畴的随机河外磁场触发 ${\mathbf{乙}}_{\mathrm{分机}}$。由于存在着银河外背景光（EBL），这是宇宙演化过程中所有星系发出的红外/光学/紫外线辐射，因此当VHE光子从EBL光子散射时，${Ë}^{+}{Ë}^{-}$可以创建一对，从而导致源的亮度大大降低。在存在光子-ALP振荡的情况下，情况有所不同，因为光子有时以真实的光子形式传播，有时以ALP形式传播。由于ALP不与EBL相互作用，因此有效光学深度会有所降低。但是，结果是，相对于传统物理学的预测，光子生存概率得到了极大提高，从而大大提高了VHE波段中的光子透明性，因此相应的视界会大大扩展。尽管所有这些都是众所周知的，并且已经进行了详细的研究（De Angelis等，2011，2013a），但是在足够高的能量下，光子弥散对宇宙微波背景（CMB）的新影响变得非常重要。本文的目的是系统地考虑它。实际上，与此相关联的是两种截然不同的能级。一个是${\mathcal{Ë}}_H=\mathcal{Ø}（5\mathrm{电视}）$以上所讨论的效果开始变得占主导地位，使单一的光束传播过程的随机的实现-唯一的那些可观察-表现出小的能量振荡：这是一个关键的预测我们的模型的。另一个能级是${\mathcal{Ë}}_{\mathrm{当量}}$ 在此之上，振荡长度变得小于的相干长度 ${\mathbf{乙}}_{\mathrm{分机}}$：通常 ${\mathcal{Ë}}_{\mathrm{当量}}=\mathcal{Ø}（40\mathrm{电视}）$具有很大的不确定性。因此，以前使用的类域模型${\mathbf{乙}}_{\mathrm{分机}}$ 通常会在上面给出错误的结果 ${\mathcal{Ë}}_{\mathrm{当量}}$ 还有一个更现实的模型 ${\mathbf{乙}}_{\mathrm{分机}}$变得引人注目，就像作者最近开发的那样。值得注意的是，我们已经能够得出相应的光子生存概率$P_{\gamma \to \gamma }^{\mathrm{碱性磷酸酶}}（{\mathcal{Ë}}_0，ž）$ 分析准确地达到观察到的能量${\mathcal{Ë}}_0=1000\mathrm{电视}$ 然后红移到 $ž=2$，这一事实大大缩短了本文提出的结果的计算时间。具体来说，对于7种模拟blazar，我们展示了$P_{\gamma \to \gamma }^{\mathrm{碱性磷酸酶}}（{\mathcal{Ë}}_0，ž）$ 沿着1000个随机实现与 ${\mathcal{Ë}}_0$，用于z的不同值和模型参数的四个值。我们的预测可以通过CTA，HAWC，GAMMA-400，LHAASO，TAIGA-HiSCORE和HERD等新一代γ射线观测站进行检验。最后，对于我们的猜测值${米}_{\mathrm{一种}}$ 和 $G_{\gamma \gamma \mathrm{一种}}$ 在DESY升级ALPS II，计划的实验IAXO，STAX和ABRACADABRA以及Avignone及其合作者开发的其他技术中，可以检测到我们的ALP。