Final-REVISION “Differentiating dilatons from axions by their mixing with photons”

Abstract The quanta of scalar fields like the dilaton (ϕ) of scale symmetry origin and those of pseudoscalar fields like the axion (' ϕ ′) of Peccei–Quinn symmetry origin couple to di-photons through dimension-5 operators. In a magnetized medium (MM), they in principle can interact with the two transverse (A, A ‖, ⊥) and one longitudinal (A₋ A L) degree of freedom of photons (γ) as long as the total spin is conserved. However, of ϕ and ' ϕ ′, only one interacts with A₋ A L. We found that the ambient external magnetic field B and media break the intrinsic Lorentz symmetry of the system affecting the dispersion relation of the propagating modes. The boost and the rotational symmetry along and around B are however the ones that are preserved. Invoking C, P, and T symmetries, we analyze the mixing dynamics of ϕ γ and ' ϕ ′ γ systems and the structural difference in their mixing pattern. It is noted that while the ϕ γ mixing matrix is 3 3 3 × 3, the ^ ϕ ′ γ is governed by a 4 4 4 × 4 mixing matrix. Using the exact solutions of both systems in MM, we estimate the strength of the electromagnetic (EM) signals available due to these interactions, which are found to be different in strength. We conclude by commenting on (a) the possibility of detecting this difference in polarimetric observables of the EM signal, (b) the implications of these different mixing patterns with respect to the minimum detectable signal for astrophysical observations, and (c) the variation in the energy of the dispersed photons of different polarization with the variation in B.