Behavior of axion-like particles in smoothed out domain-like magnetic fields

Abstract

Basically, in certain circumstances axion-like particles (ALPs) substantially enhance the photon survival probability $P_{\gamma \to \gamma }(\mathcal{E})$ of a beam emitted by a far-away source through the mechanism of photon-ALP oscillation ($\mathcal{E}$ denotes the energy). But in order for this to work, an external magnetic field $\mathbf{B}$ must be present. In several cases $\mathbf{B}$ is modeled as a domain-like network with `sharp edges': all domains have the same size $L_{\mathrm{dom}}$ (set by the $\mathbf{B}$ coherence length) and the same strength B, but the direction of $\mathbf{B}$ changes randomly and abruptly from one domain to the next. It is obviously a highly mathematical idealization wherein the components of $\mathbf{B}$ are discontinuous across the edges (whence the name sharp edges). It is therefore highly desirable to go a step further, and to find out what happens when the edges are smoothed out, namely when the abrupt change of $\mathbf{B}$ is replaced by a smooth one. Moreover, this step becomes compelling when the photon-ALP oscillation length $l_{\mathrm{osc}}$ turns out to be comparable to -- or smaller than -- $L_{\mathrm{dom}}$, because in this case the photon survival probability $P_{\gamma \to \gamma }(\mathcal{E})$ critically depends on the domain shape. In the present paper we propose a smoothed out version of the previous domain-like structure of $\mathbf{B}$ which incorporates the above changes, and we work out its implications. Even in the present case we are able to solve analytically and exactly the photon/ALP beam propagation equation inside a single smoothed-out domain, thereby evaluating the corresponding $P_{\gamma \to \gamma }(\mathcal{E})$ exactly. Our results is of particular importance in view of the new generation of gamma-ray detectors, since in such a situation $l_{\mathrm{osc}}\lesssim L_{\mathrm{dom}}$ occurs just above the TeV scale.

30 pages, 14 figures. This version matches the published paper: Phys. Rev. D 98, 043018 (2018)

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