1003.4023 (Harry J. Lipkin)

Simple quantum mechanics explains GSI Darmstadt oscillations Even with
undetected neutrino; Momentum conservation requires Same interference
producing oscillations in initial and final states    [PDF]

Harry J. Lipkin

GSI experiment studying oscillations in K-capture decay of radioactive ion
investigates neutrino masses and mixing without detecting neutrino. Even when
neutrino is not detected quantum mechanics relates initial and final states.
The basic physics is very simple. Neutrinos emitted in beta decay are coherent
linear combinations of states with different masses, different momenta and same
energy. Since the weak interaction producing the neutrino conserves momentum,
the initial state before the transition must also contain a coherent linear
combination of states with the same momentum difference and a well defined
relative magnitude and phase. A one-particle state with a definite momentum
difference also has an easily calculated energy difference. In the time
interval between creation of the ion and its decay a linear combination of two
states with different energies oscillates in time. Measuring the oscillation
period gives a value for the difference between squared neutrino masses of the
two neutrino mass eigenstates. The value obtained from a crude approximation
with no free parameters for this "two-slit" or "which path" experiment in
momentum space differs by less than 10% from the result observed in the KAMLAND
experiment. Observing only ion disappearance without detecting neutrino avoids
signal suppression by low neutrino absorption cross section

View original: http://arxiv.org/abs/1003.4023