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Dark photons can oscillate into Standard Model (SM) photons via kinetic
mixing. The conversion probability depends sensitively on properties of the
ambient background, such as the density and electromagnetic field strength,
which cause the SM photon to acquire an in-medium effective mass. Resonances
can enhance the conversion probability when there is a level-crossing between
the dark photon and background-dependent SM photon states. In this work, we
show that the widely used Landau-Zener (LZ) approximation breaks down when
there are multiple level-crossings due to a non-monotonic SM photon potential.
Phase interference effects, especially when the dark photon mass is close to an
extremum of the SM photon effective mass, can cause deviations from the LZ
approximation at the level of a few orders of magnitude in the conversion
probability. We present an analytic approximation that is valid in this regime
and that can accurately predict the conversion probabilities in a wide range of
astrophysical environments.
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