  Many extensions of the Standard Model of particle physics and in particular
superstring and superbrane theories predict the existence of axion-like
particles (ALPs). ALPs are very elusive, extremely light and interact primarily
with photons. In the presence of an external magnetic field two effects show
up: (i) photon-ALP oscillations and (ii) a change of the photon polarization
state. The astrophysical context represents the best opportunity to get
indirect evidence for the ALP existence thanks to various effects that the
photon-ALP interaction produces in the sky. Great attention has been paid so
far to photon-ALP oscillations, since they modify the transparency of the
crossed media at very high energies and so the final spectra of faraway sources
exhibit a flux excess and a characteristic oscillatory behavior. Two hints at
the ALP existence have hitherto been discovered. But less interest has been
attracted by the modification of the photon polarization. In this paper we
address it in the X-ray and in the high energy (HE) bands. Specifically, we
analyze the photon degree of linear polarization and the polarization angle
induced by the photon-ALP interaction for photons generated in the central
region of two galaxy clusters: Perseus and Coma. We find a substantial
departure from conventional physics in both considered bands. We conclude that
the ALP-induced polarization effects are more likely detectable with the
proposed missions like COSI (approved to launch), e-ASTROGAM and AMEGO in the
HE range. Still, possible ALP-induced effects on photon polarization could also
be detected by IXPE (already operative) and by the proposed eXTP, XL-Calibur,
NGXP and XPP in the X-ray band.
