LAUSR

Surveys of diffuse $\gamma$-ray in the interstellar medium (ISM) can be used to probe hydrogen-antihydrogen oscillations, by detecting the $\gamma$-ray emission from antihydrogen annihilation. A bound on the oscillation parameter $\delta$ was originally derived by Feinberg, Goldhaber and Steigman (1978). In this paper, we re-visit the original derivation by performing a more detailed analysis that (1) incorporates suppression effects from additional elastic and inelastic processes, (2) treats the ISM as a multi-phase medium, and (3) utilises more recent $\gamma$-ray data from the Fermi Large Area Telescope. We find that suppression from elastic scattering plays a more important role than previously thought, while the multi-phase nature of the ISM affects how the $\gamma$-ray data should be utilised. We derive a more accurate bound on the oscillation period that is about an order of magnitude weaker than the older bound.