Magnetized matter effects on dilaton photon mixing

Dilatons ($\\phi(x)$) are a class of bosonic scalar particles associated with\nscaling symmetry and its compensation (under the violations of the same). Due\nto two photon coupling, they can produce optical signatures in a magnetic\nfield. In vacuum or plain matter they couple to one of the transversely\npolarized state of the photon. But in a magnetized matter, they couple to both\nthe transversely polarized state of photon (due to emergence of a parity\nviolating part of photon self energy contribution from a magnetized matter). A\npart of this work is directed towards understanding the issue of mixing of\nscalar with various polarizations states of photon in a medium ( magnetized or\nunmagnetized ) due to the constraints from different discrete (CPT) symmetries\nassociated with the interaction. Based on these symmetry aided arguments, the\nstructure of the mixing matrix is found to be $3 \\times 3$. Thus there exists\nnon-zero finite probabilities of oscillation between different polarization\nstates of photon to dilaton. Our analytical and numerical analysis show no\nexistence of periodic oscillation length either in temporal or spatial\ndirection for most general values of the parameters in the theory. Possible\nastrophysical consequences of these results, those can be detected through\nobservations are discussed.\n