Why a splitting in the final state cannot explain the “GSI oscillations” measured at the GSI Experimental Storage Ring

In this article, I provide a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive quantum-field-theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the double-slit experiment using photons, $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering, and charged-pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only standard model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the quantum beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.

Figure 1

The diagrams contributing to $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the SM.

Figure 2

The Feynman diagram for the GSI experiment.

Figure 3

Type I (left) and type II (right) of the QBs settings.