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 m 2 2 − m 1 2 = 2.22 ( 3 ) × 1 0 − 4 eV 2 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.