Is the GSI anomaly due to neutrino oscillations? - A real time perspective -

We study a model for the "GSI anomaly" in which we obtain the time evolution of the population of parent and daughter particles directly in real time, considering explicitly the quantum entanglement between the daughter particle and neutrino mass eigenstates in the two-body decay. We confirm that the decay rate of the parent particle and the growth rate of the daughter particle do \emph{not} feature a time modulation from interference of neutrino mass eigenstates. The lack of interference is a consequence of the orthogonality of the mass eigenstates. This result also follows from the density matrix obtained by tracing out the unobserved neutrino states. We confirm this result by providing a complementary explanation based on Cutkosky rules applied to the Feynman diagram that describes the self-energy of the parent particle.