Time-modulation of entangled two-body weak decays with massive neutrinos

In recent experiments at the GSI, Darmstadt, time-modulated orbital Electron Capture (EC) decays of H-like ¹⁴⁰Pr⁵⁸⁺, ¹⁴²Pm⁶⁰⁺, and ¹²²I⁵²⁺ ions with one electron in the K-shell, coasting in the ESR storage ring with velocity β=0.71, were observed. The EC-branches show exponential decay curves time-modulated with period T=7.06(8) s and amplitude a=0.18(3) for ¹⁴⁰Pr decays, T=7.10(22) s and a=0.23(4) for ¹⁴²Pm decays, and T=6.04(6) s and a=0.19(3) for ¹²²I (preliminary) decays in the laboratory frame. The simultaneously measured β⁺ branch of ¹⁴²Pm shows no modulation with a<0.03. We discuss here as origin of the modulation quantum beats produced by the superposition of massive neutrino, mass eigenstates emitted in the entangled two body weak decay. From the modulation frequency a value for the difference of the quadratic mass values is deduced, which is 2.9 times larger than the value derived by the KamLAND antineutrino oscillation experiment. The origin of the small modulation amplitudes is discussed as the result of a partial restoration of the interference terms which are expected to cancel for the usual assumed unitarity of the neutrino flavor mixing matrix.