Kinematics and Quantum Field Theory of the Neutrino Oscillations Observed in the Time-modulated Orbital Electron Capture Decay in an Ion Storage Ring

Abstract

According to the recent experimental data of a GSI--experiment, the rate of the number of daughter ions ${}^{140}{\mathrm{Ce}}^{58+}$, produced by a nuclear K--shell electron capture (EC) of the H--like ion ${}^{140}{\mathrm{Pr}}^{58+}$, is modulated in time with a period $T_d=(7.06\pm 8)$seconds. We explain this phenomenon by neutrino--flavour mixing and show that this can be understood within standard quantum field theory and derive a value for the squared mass difference $\Delta m_{21}^2=m_2^2-m_1^2=(0.763\pm 8)\cdot 10^{-4}{\mathrm{eV}}^2$. This proves that such processes provide a precise method to investigate neutrino--flavour mixing.

Comments: 17 pages